Linköping University | Department of Management and Engineering
Master’s thesis, 30 credits| Mechanical Engineering
Spring 2020 | ISRN LIU-IEI-TEK-A--20/03936--SE
Modelling, evaluation and assessment
of welded joints subjected to fatigue
Author:
Prajeet Rajaganesan
Supervisors:
Amir Alizadeh
Sigma Industry
Jari Mäkinen
Sigma Industry
Carl-Johan Thore
Linköping University
Kjell Simonsson
Linköping University
Examiner:
Abstract
Fatigue assessment of welded joints using finite element methods is becoming very common.
Research about new methods is being carried out every day that show a more accurate estimation
of the fatigue life cycle than the previous ones. Some of these methods are investigated in this
thesis for a thorough understanding of the weld fatigue evaluation process.
The thesis study presents several methods as candidates for analysis of selected case studies for
comparison. The sensitivity of methods towards FE model properties was studied. The ease of
implementation for further automatization of the method was highly considered from the early
stages of the project. A comparison study amongst feasible methods was then performed after
analysis.
The selected three case studies provided a wide range of difficulties in terms of geometry and
loading and made them suitable for the methods to be evaluated. It should be noted that case
studies only with fillet welds were considered during the literature study and analysis.
Implementation of some methods on a case study where they have not previously been tested
before gave a challenging task during the analysis phase. The proposed method after comparison
and ranking of the methods based on several criteria such as accuracy, robustness, etc. was the hot
spot stress method. The main advantages of this method are its low computational time, less
complexity during both pre- and post-processing, and the ability to work for both solid and shell
models.
Finally, the report gives a walk-through of several functionalities of the post-processor tool built
to enhance workflow for the hot spot based fatigue assessment of welds. Pseudo-codes for some
functions of the tool are given for clarity. A summary of the workflow is presented as a flowchart.
The outputs of the case studies were then evaluated using the tool and compared with the manual
evaluation to check the effectiveness of the tool on different scenarios. The tool shows flexibility
in handling different types of weld geometry with good agreement to the results obtained manually
but only for welds lying on a flat surface. Some of the advantages of the tool are its capability to
handle multiple welds simultaneously and the flexibility to the user in selecting the way the results
are presented. Most of the postprocessing steps are automatized, while some require user inputs.
i
Table of contents
Abstract ................................................................................................................................. i
Preface ..................................................................................................................................iv
List of abbreviations ............................................................................................................. v
List of symbols ...................................................................................................................... v
1
2
Introduction ................................................................................................................... 1
1.1
Background .................................................................................................................................................. 1
1.2
Problem definition ...................................................................................................................................... 2
1.3
Methodology ................................................................................................................................................ 2
1.4
Delimitations................................................................................................................................................ 3
1.5
Other considerations .................................................................................................................................. 3
Theory ............................................................................................................................ 5
2.1
Fatigue in welded joints.............................................................................................................................. 5
2.2
Factors influencing fatigue in welds ......................................................................................................... 6
2.2.1
Fatigue loading ................................................................................................................................... 6
2.2.2
Geometry............................................................................................................................................. 7
2.3
Fatigue resistance curves – S-N curves ................................................................................................... 7
2.4
Stress analysis approaches.......................................................................................................................... 8
2.4.1
Introduction ........................................................................................................................................ 8
2.4.2
Nominal stress approach .................................................................................................................. 9
2.4.3
Structural stress approaches ...........................................................................................................10
2.4.4
Effective notch stress approach ....................................................................................................18
2.5
3
Summary of approaches ...........................................................................................................................19
Finite element analysis ................................................................................................ 21
3.1
3.1.1
3.2
3.2.1
3.3
3.3.1
Case study 1 ...............................................................................................................................................21
Results ................................................................................................................................................23
Case study 2 ...............................................................................................................................................29
Results ................................................................................................................................................30
Case study 3 ...............................................................................................................................................31
Results ................................................................................................................................................32
4
Observations and discussion ....................................................................................... 35
5
A plug-in tool for weld fatigue assessment.................................................................. 39
5.1
Introduction ...............................................................................................................................................39
5.2
User inputs .................................................................................................................................................39
5.3
Methodology ..............................................................................................................................................40
5.3.1
Segregation and classification of welds ........................................................................................41
5.3.2
Determination of type of weld geometry .....................................................................................42
ii
6
7
8
5.3.3
Extraction of stresses ......................................................................................................................48
5.3.4
Reporting the results as plot...........................................................................................................48
Results and comparison study ..................................................................................... 49
6.1
Case study 1 ...............................................................................................................................................49
6.2
Case Study 2 ...............................................................................................................................................50
6.3
Case study 3 ...............................................................................................................................................52
Conclusions and summary........................................................................................... 55
7.1
Conclusions – Theory ..............................................................................................................................55
7.2
Conclusions – FEA...................................................................................................................................55
7.3
Summary – Plug-in tool for weld fatigue assessment..........................................................................56
Recommendations ....................................................................................................... 58
References ........................................................................................................................... 59
Appendix A – Method scoring matrix ................................................................................ 61
Appendix B – Workflow summary ...................................................................................... 62
Appendix C – Weld fatigue assessment tool interface ....................................................... 63
Appendix D – Structural stress approaches for further scope ............................................ 64
iii
Preface
The work presented in this master thesis was conducted at Sigma Industry in Stockholm between
February and October 2020. The project was initiated and carried out within the Technical
Calculation & Testing department of Sigma Industry. This thesis is a part of the requirements for
the master’s degree in Mechanical Engineering at Linköping University, Sweden.
I would like to acknowledge and thank my supervisors at Sigma Industry, Amir Alizadeh and Jari
Mäkinen for their excellent guidance, strong technical support, and helpful discussions throughout
the thesis work. I would also like to express my gratitude to Daniel Tanner at Sigma Industry for
his constant help and encouragement. I gratefully acknowledge everyone at Sigma Industry East
North for providing me with the best learning experience.
I would also like to thank my supervisor at Linköping University, Carl-Johan Thore for thoroughly
studying my work and contributing to the report. I would like to thank my examiner, Kjell
Simonsson for his help and feedback on this thesis.
Finally, I would like to express my profound gratitude to my family and friends for their everlasting
support and patience.
Linköping, October 2020
Prajeet Rajaganesan
iv
List of abbreviations
IIW
FEA
FEM
2D
3D
GUI
WIN32COM
TTWT
CAE
SS
HSS
LSE
S-N
ENS
SAE
CAFL
VAFL
LEFM
E2S2
KPI
International Institute of Welding
Finite Element Analysis
Finite Element Method
Two Dimensional
Three Dimensional
Graphical User Interface
Python package
Through Thickness at the Weld Toe
Computer-Aided Engineering
Structural stress methods
Hot Spot Stress
Linear Surface Extrapolation
Stress-Life
Effective Notch Stress method
Society of Automotive Engineers
Constant Amplitude Fatigue Loading
Variable Amplitude Fatigue Loading
Linear Elastic Fracture Mechanics
Equilibrium Equivalent Structural Stress
Key Performance Index
List of symbols
∆𝜎
R
𝜎𝑚
∆𝜎𝑛𝑜𝑚,𝐻𝑆𝑆
t
𝑡𝑟𝑒𝑓
n
∆𝑆𝑒𝑞
𝜎𝑆
𝜎𝑚
𝜎𝑏
∆𝑆𝑠
𝑟
FAT
𝜑𝑄
Stress range
Stress ratio
Mean stress
Stress computed from nominal stress or Hot spot method
Thickness of the welded plate
Reference thickness; 25 mm in IIW
Thickness exponent
Equivalent structural stress parameter
Structural stress
Membrane stress
Bending stress
Structural stress parameter
Bending ratio
Fatigue strength at 2 ∙ 106 cycles
Coefficient of risk failure
v
1 Introduction
This master thesis was initiated and carried out as a co-operation between Sigma Industry East
North and Linköping University and aims for developing standardized methods to assess welded
joints that are subjected to fatigue loading.
1.1
Background
Fatigue is the failure of a structure due to cyclic loading and is one of the important criteria for the
design of a welded structure. Structures involved in transportation such as automobiles, ships,
airplanes, offshore structures, bridges, cranes, etc. that are subject to fluctuating loads are prone to
fatigue failure as time progresses. The phenomenon originates at the microscopic level, where local
damages evolve into a macroscopic crack, and then leads to final failure. It is usual for the damage
to initiate at a location consisting of sudden geometrical change such as a notch where there is
stress concentration or at a material defect such as a material inhomogeneity within the weld [1],
[2].
Fatigue of welds as a process is known to be highly localized as the fatigue life of a structure is
majorly influenced by the local parameters such as geometry, loading, and material characteristics
of the region. Structures under repetitive cyclic loading are known to possess critical locations
prone to fatigue failure at the welded joints due to high stress concentration. The industries should
thus employ a method that accurately estimates the fatigue life of a welded structure regardless of
the geometrical or loading complexities involved [1], [2], [3].
There are two approaches to fatigue assessment in welded structures, viz. global and local methods.
In both of them, the fatigue cycles or the crack growth is determined by the S-N curve approach
or fracture mechanics approach. The S-N curve approach has been focused on this thesis project,
where most of them come under local methods. The local methods provide better results than the
global methods as the fatigue of welds is a localized process. The S-N curve approach branches
into two most used methods that are the focus of this project: the structural stress approaches and
the effective notch stress approach. Both are known for providing a reliable estimation of fatigue
life cycles from the stress results of a Finite Element Analysis (FEA) [1].
IIW recommendations [4] provide the reference classes for both sub-branches of the S-N curve
approaches under several geometries and loading scenarios, based on which the stress from an
FEA can be plugged in to obtain the fatigue life cycle. The reference classes for different geometry
and loading conditions correlate to different stress-life curves. The curves are based on many
fatigue experiments that automatically considers the effect of material defects.
Different methods require different post-processing procedures to arrive at a result, and the
execution of the steps in the right way determines the level of accuracy. Most of them have
straightforward calculations, while a few of them are complex due to the way the results are
extracted from the analysis or due to complicated calculations. Automatizing these repetitive steps
makes the evaluation of multiple welds faster. However, to do that for any weld type, a multiple
1
number of times, one requires a plug-in tool in Abaqus1 that can automatize most of the postprocess, which will be the result of this thesis project.
1.2 Problem definition
The fatigue assessment methods presented in this report are stress-based, and almost all of them
are functionally different involving different procedures during both pre- and post-processing.
Even when some methods are computationally cheap, they are still highly time-consuming during
FE-modelling and post-processing of the FE results when complex calculations are involved.
It is the work of the engineer to manually extract the stresses from a read-out point and plug it in
a formula to obtain the stress required to determine fatigue life. For a single weld, this might be
simple, but when there are multiple welds or when a complex weld geometry is involved, it will be
beneficial to automatize the process to minimize the time taken. However, the method for
automatization should be selected based on a combination of several aspects of the method aside
from just the computational time or level of complexity.
The selected methods should be compared based on aspects that influence the performance and
the effectiveness of the tool built for automatization. The resulting method that is ranked higher
among others based on those aspects should be implemented as a program scripted by using
Python for Abaqus. The program should be checked for effectiveness and efficiency through a
comparison of manually obtained results to the automatized results. The re-evaluation of the case
studies using the tool will be used for inspection for possible bugs or flaws inside the tool to be
fixed.
Therefore, the objectives of this thesis can be presented as the following questions:
•
•
•
Which method outranks other methods based on Key Performance Indexes, KPIs that
makes it suitable for implementation as a post-processing tool for assessing weld fatigue?
How can the plug-in tool be built in Abaqus and how flexible can it be made to handle
different types of welds and element types i.e., shell, and solid elements?
How effective is the tool built based on how it is influenced by finite element properties
and how does it compare with the manual way of result extraction?
1.3 Methodology
Methods considered for fatigue assessment in this project are different from each other in several
ways, and the procedure followed in those to arrive at the results must be studied and understood
to avoid mistakes. A literature study was performed to find the existing methods of weld fatigue
assessment and to gain an understanding of the theory and challenges behind those methods. A
preliminary summary from the theoretical study of some major methods was presented, listing all
their advantages and disadvantages. The inaccurate ones were eliminated.
The simulation process was carried out in Abaqus, while the calculation and output analysis were
carried out in MATLAB2. Several case studies consisting of geometries of different levels of
complexity and approaches were used to gather reference data. The case studies were then recreated
1
2
https://www.3ds.com/products-services/simulia/products/abaqus/
https://www.mathworks.com/products/matlab.html
2
in the solver to be compared again based on properties like accuracy, post-processing time, preprocessing workload, and so on.
The aim of recreating the model, simulating and evaluating it using different methods was to obtain
a good understanding of the procedures followed to correctly apply the methods to different
geometry, to understand the difficulty behind applying the procedures, and to check how the mesh
properties influence the results obtained. This process determined the degree of the
conservativeness of the methods which was essential during the comparison and ranking.
The development of the easy-to-use plug-in tool in Abaqus formed one of the primary objectives
and the result of the thesis project. Python scripting for Abaqus was used to create the plug-in tool.
Several functionalities of a GUI that can be created using Python was studied and explored to
create a versatile, easy-to-use tool.
The final part will show the validation of the tool and its desired properties by reevaluating the case
studies using the tool for fatigue assessment. A thorough comparison of the manual simulation and
the automatized one was done where the possible improvements were identified and implemented.
Further enhancements for the tool in the future were also established as recommendations.
1.4 Delimitations
The welded joints used in this project are As-welded types of joints which imply that after-weld
treatment effects and high strength steels were not considered. Constant amplitude loading was the
type of loading used in the case studies referred to in this project. High cycle fatigue was the only
type of fatigue within the scope of this project as stress-based approaches were considered for
fatigue assessment.
Heat-induced residual stress from welding or metallurgical and heat-affected zones were not
considered in this thesis. Multiaxial fatigue was also not within the scope of this thesis. The effects
of shear stresses are assumed to be minimal hence, only the first principal stress will be used in the
static and fatigue analyses.
One of the limitations involved with Abaqus is related to its Python version and the pre-installed
libraries. As the Python version installed with the software varies with the software version, it is
impossible to implement some functions due to the unavailability of some in-built libraries with
older versions of Python.
1.5 Other considerations
The thesis work does not raise any questions regarding gender, age, ethnicity, sexual identification,
or religious belonging. Furthermore, no sustainability related questions are in focus in this work,
which has been carried out in accordance with the Swedish law.
3
4
2 Theory
This Chapter provides an overview of the basic theory behind fatigue in welds through the literature
considered for this project. The Chapter describes theory behind all the methods considered for
preliminary comparison. Also, Appendix D – Structural stress approaches for further scope
includes theory for methods that can be implemented in the future work.
2.1 Fatigue in welded joints
There are three stages to Fatigue failure:
1. Crack initiation phase
2. Crack propagation phase
3. Final rupture
The micro- and macro-phenomena stages of fatigue can be inferred from [2] as shown in Figure 1.
Figure 1: Micro- and macro- phenomena stages of fatigue, picture redrawn from [2]
The first stage, the crack initiation phase, consists of micro-cracks formed at the surface of a
structure where the initiation time depends on the level of material defects and stress. When welded
joints are considered, this phase has little significance compared to a nonwelded detail where it is
essential in the determination of its fatigue life. The already available weld imperfections result in
early crack initiation, usually in the first loading cycle itself [1], [2].
The locations of imperfections in the welds are more prone to crack initiation than the regions of
the base material. The crack either starts from the weld root or weld toe and propagates through
the thickness of the plate. The amount of penetration of the weld will determine if the failure will
start from the weld toe or root. Usually, weld toe failure occurs when the weld penetration is
complete and root failure when it is incomplete. One of the solutions for increasing the number of
cycles before crack initiation is to conduct a post-weld treatment in the weld toe, which has the
capability of reducing the chances of cracks initiating from the weld toe [1].
The crack propagation phase is the second stage. Here the growth of the crack has progressed to
macroscopic size due to strain occurring in the perpendicular direction of loading. The propagation
of macro cracks in this phase is stable until the crack size reaches a critical limit above which it
tends to become unstable and ultimately leads to the final rupture. This propagation rate is highly
dependent on the material properties in the thickness region, whereas the crack initiation is surface,
material and environment interaction dependent [1], [2], [5].
The crack is most often initiated due to local stress concentration created by a sudden change in
geometry like holes or notches. So, one needs to understand how these properties affect the fatigue
life of a structure, which leads to the next part of the theory.
5
2.2 Factors influencing fatigue in welds
Many factors affect the fatigue strength of a structure, including the magnitude and frequency of
loading, geometric details, weld imperfections such as voids, insufficient penetration and notches,
material flaws and discontinuities, surface quality, and environment. However, the two most
important factors are loading and geometry.
2.2.1
Fatigue loading
Fatigue loading is one of the significant factors that affect the fatigue life of the structure. It is the
process of inducing fluctuating stresses through varying the applied load by changing pressure,
vibrations, temperature, or wave loads. There are two types of fatigue loading: Constant Amplitude
Fatigue Loading (CAFL) and Variable Amplitude Fatigue Loading (VAFL). A structure is
commonly under variable amplitude loading. The stress ranges in a VAFL are generated by varying
amplitudes of loads. Other important factors that determine the fatigue life of the structure, such
as the mean stress value and the sequence of loading, are also constantly changing in a VAFL. For
simple design calculations, constant amplitude stress ranges are utilized throughout the thesis work
[6].
As can be inferred from Figure 2, the stress range, ∆𝜎, is one of the important parameters
influencing fatigue life. Another important parameter is the stress ratio, R, which is the ratio of
minimum stress to the maximum stress indicating the effect of mean stresses, 𝜎𝑚 . The stress ratio
is considered zero for most of the thesis work except for one case where the stress ratio is -1 due
to fully reversed loading condition.
Figure 2: Constant amplitude fatigue loading, CAFL. Redrawn from [6]
6
2.2.2 Geometry
Fatigue is directly influenced by the geometrical aspects of a structure, such as dimensions, crack
location, and complexity of the structure. The main reason for stress concentration is the presence
of a sudden change in geometry. Such changes must thus be reduced during the design phase for
a better fatigue life of the structure [6].
The fatigue strength of a weld joint is highly affected by the thickness of the welded geometry. This
was confirmed by T.R. Gurney, 1968 [1] through experimental results and analysis. He concluded
that the increase in thickness resulted in the decrease of fatigue strength of the weld due to the
increase in residual stress caused by welding process. A so-called thickness correction factor was
introduced in 1995 by T. R. Gurney [6] where the thickness reduction factor for thicker plates is
given by
𝑡𝑟𝑒𝑓 𝑛
)
∆𝜎𝑡 = ∆𝜎𝑛𝑜𝑚,𝐻𝑆𝑆 (
𝑡
where ∆𝜎𝑛𝑜𝑚,𝐻𝑆𝑆 is the fatigue strength from nominal stress or hot spot method, 𝑡𝑟𝑒𝑓 is the
reference thickness, and 𝑛 is the thickness exponent
2.3 Fatigue resistance curves – S-N curves
There are two approaches used for the fatigue assessment during the designing phase [6]:
•
•
Classification approach (also known as the S-N curve approach)
Fracture mechanics approach based on Linear Elastic Fracture Mechanics (LEFM)
The classification method utilizes S-N curves with fatigue design classes presented as a logarithmic
relationship between stress range and the number of stress cycles to failure, as shown in Figure 3.
These values are obtained through experiments with samples subjected to variable stresses of both
constant and variable amplitudes. This standardized fatigue design method assumes that the
material behavior of the whole structure and the fatigue-critical area is elastic [6], [7].
The welded structure details are divided into fatigue design classes, also known as FAT, along with
a number indicating the nominal stress range at 2 million cycles at a survival probability of 97.7%.
The fatigue strength curve for every standard detail has a knee point, which corresponds to the
fatigue or endurance limit. A specimen with applied stress less than the fatigue limit can work up
to an infinite number of load cycles without failing. The fatigue strength curves that are
recommended by IIW will be used throughout this thesis project [6], [7], [4].
The fracture mechanics approach was introduced by Paris [1] and represents the fatigue crack
propagation by connecting the propagation rate to the stress intensity at the tip of the crack, which
is prone to cyclic stress. The method is one of the basic approaches and is widely used nowadays
as it can describe crack propagation while the S-N curve approach cannot. However, the approach
assumes the size of the initial crack, which is not possible to measure during the design phase and
needs more research in certain other areas [1].
There is another type of S-N curve called the Master S-N curve which is used in structural stress
methods involving stress linearization through the thickness of the weld plate such as Dong’s
approach [8]. The Master S-N curve can be expressed by:
7
𝑙𝑜𝑔𝑁𝑓 = 12.88 − 3.08𝑙𝑜𝑔∆𝑆𝑒𝑞
where ∆𝑆𝑒𝑞 is the equivalent structural stress parameter. This curve can be used for all types of
loading or geometry conditions but the structural stress must be obtained from Dong’s approach
[8].
Figure 3: S-N curve for fatigue classes 100 and 225, normal stress, standard applications; picture redrawn from [6]
2.4 Stress analysis approaches
These methods make use of the stress obtained from an analysis to determine fatigue life or fatigue
strength. Some of these methods are presented in this Section.
2.4.1 Introduction
There are two ways of approaching fatigue life assessment for welded joints:
•
•
Global methods
Local methods.
Global methods are based on stresses obtained from strength assessments considering the external
forces and moments acting on a critical cross section. The macro geometrical effects are not
considered in this approach. Local methods consider local parameters such as local stresses or
strain from local geometry at a critical location. Variants of both global and local approaches used
within industry are shown in Figure 4 [1].
8
Figure 4:Global and local approaches for fatigue life assessments; picture redrawn from [1]
A well-known global method is the nominal stress method which is based on the average stress in
the cross-section where the local effects are neglected. Local methods include structural stress,
notch stress, and notch strain approaches. The different types of stresses in weld fatigue and the
stress distribution along the thickness of the welded plate are shown in Figure 5.
Figure 5: Stress distribution through the thickness of a welded plate and weld fatigue stresses. Redrawn from [6]
2.4.2 Nominal stress approach
The nominal stress approach is the simplest and most widely used method for steel structures and
is also standardized for different types of welds. This method disregards local stress raising effects
such as nonlinear stress peak and residual stress while calculating the average stress from a crosssection using a linear stress assumption. However, those influencing factors, including
misalignment, are considered in the design codes and recommendations [1], [3].
The nominal stress method is easy to implement for practical applications. However, the limitation
of this method is the required classification of structural details. The welds are classified by their
joint geometry and loading conditions. Selecting a specific S-N curve for an application can lead to
9
an error when there are differences in dimensions or loading in the application compared to the
reference data. The nominal stress method is thus unsuitable for complex geometry or loading
conditions as it might be hard to implement and will result in lower accuracy leading to costlier
errors during design [9].
The fatigue life calculated from this method represents the total fatigue life of the component and
does not differentiate between crack initiation and propagation life. The method does not provide
guidelines on how to use FEA for calculating nominal stress, but it can be assumed that the stress
is obtained at a distance of 1 or 1.5 times the plate thickness away from the weld toe which makes
it mesh dependent. The effect of residual stresses was included by shifting the S-N curves down to
a slope of 2.7 from 3 but still, it does not help to account for the actual residual stress for the
specific weld detail [9].
Considering all the advantages and disadvantages of the nominal stress method, it was decided to
not take this method forward to the next step of comparison with the other methods due to the
compromise in the accuracy which is one of the major criteria in the ranking of the methods.
2.4.3 Structural stress approaches
Structural stress methods have in common the ability to capture the effect of geometrical
discontinuity (unlike nominal stress method) which is desired when the method must capture the
load effect due to geometrical changes. This Section gives a brief description of the basic types of
structural stress methods.
2.4.3.1
Hot spot method
The hot spot method is applicable when the geometry is complex. This method was initially
developed for pressure vessels and tubular structures and was later used for plates or non-tubular
joints in the early 1990s. The reason this method can be applied to complex geometries is that it
takes local stress concentrations and load redistributions into account and that the S-N curve for
most types of loading is available [6].
The hot spot method has become a widely used method for fatigue assessment of welded joints
over the past decade. It has evolved into a method that can provide accurate fatigue life data for a
structure [6].
Hot spots are regions that are prone to fatigue failure, and there exist two types of hot spots: Type
A and B. The types of hot spots are seen in Figure 6. The hot spots exist in the weld toe either at
the edge of the weld or along the weld. The hot spots limit the assessment to failure at the weld
toe only. Type A is present on the weld toe of the plate surface and Type B is on the weld toe of
the plate edge. Both types have their extrapolation distances that differ based on the FE mesh
being coarse or fine [6]. This will be discussed later.
10
Figure 6: Types of fatigue critical hot spots, redrawn from [6]
The dimensions and loading conditions of the component near the weld joint affect the value of
hot spot stress obtained. The procedure to determine structural stress for all the methods involve
either extraction of stress values from the surface attached to the weld toe or through linearization
of stress through the thickness of the plate. The hot spot method uses extraction of stress results
from the surface as shown in Figure 7. IIW recommendations suggest that the reference point
closest to the weld toe for stress extrapolation should be at 0.4 times the thickness of the plate to
avoid the influence of nonlinear stress from the weld notch [4].
Figure 7: Mesh and stress extrapolation direction for all hot spot types on shell and solid elements, redrawn from [4]
One of the procedures to derive the hot spot stress from an FEA is reading the stress values at two
reference points and using those to extrapolate for the stress at the weld toe. This will exclude the
notch stress as the reference points are located outside the region that is influenced by the local
weld geometry. Haibach and Oliver [10] suggested that for Type A hot spots, the distance can be
considered as a function of thickness, around 0.3 t from the weld toe. However, this project will
consider the IIW recommendations [4], which suggest 0.4 t. Type B hot spots have fixed
predetermined distances from the weld toe, and it doesn’t vary with the thickness of the welded
plate [4].
There are two major types of stress extrapolation techniques for both Type A and Type B hot
spots: linear and quadratic stress extrapolation. The linear extrapolation for Type A consists of two
subtypes for coarse mesh with higher order elements and fine mesh which is shown in Figure 8,
11
while Type B doesn’t have any subtypes. Both Type A and Type B has only one type of quadratic
extrapolation which is shown in Figure 9.
Figure 8: Linear extrapolation for fine and coarse mesh models, redrawn from [6]
Three reference points are required in the quadratic extrapolation method. For a Type A hotspot,
the reference points are located at 0.4t, 0.9t and 1.4t from the weld toe and for a Type B hotspot,
at 4, 8 and 12mm from the weld toe. This requires the model to be finely meshed at the weld toe
vicinity. It can be noted that the distances are not a function of thickness for Type B hot spot
unlike for Type A hot spot.
Figure 9: Quadratic extrapolation of Type A and B hot spots, redrawn from [6], [4]
IIW [4] recommends the following formulas for hot spot stress evaluation.
12
Type A hot spot:
•
•
Linear extrapolation
o Fine mesh with element length not more than 0.4t from the hot spot, Figure 8
left:
𝜎𝐻𝑆𝑆 = 1.67 ∙ 𝜎0.4∙𝑡 − 0.67 ∙ 𝜎1.0∙𝑡
o Coarse mesh with higher order elements having lengths equal to plate thickness,
Figure 8 right:
𝜎𝐻𝑆𝑆 = 1.50 ∙ 𝜎0.5∙𝑡 − 0.50 ∙ 𝜎1.5∙𝑡
Quadratic extrapolation
o Fine mesh and reference points as defined above. Recommended for thick-walled
structures, Figure 9 left.
𝜎𝐻𝑆𝑆 = 2.52 ∙ 𝜎0.4∙𝑡 − 2.24 ∙ 𝜎0.9∙𝑡 + 0.72 ∙ 𝜎1.4∙𝑡
Type B hot spot:
•
•
Coarse mesh with higher order elements with element size of 10 mm at hot spot, Figure 8
right:
𝜎𝐻𝑆𝑆 = 1.50 ∙ 𝜎5 𝑚𝑚 − 0.50 ∙ 𝜎15 𝑚𝑚
Fine mesh and quadratic extrapolation, Figure 9 right:
𝜎𝐻𝑆𝑆 = 3 ∙ 𝜎4 𝑚𝑚 − 3 ∙ 𝜎8 𝑚𝑚 + 𝜎12 𝑚𝑚
There are two challenges when it comes to the hot spot method. The first one is estimating the
structural hot spot stress by applying the right mesh properties as it is known to be sensitive to
mesh size near the weld toe. The second is selecting the right fatigue design curve for the loading
and geometry conditions. There are nine fatigue design S-N curve groups based on geometry and
loading type in IIW for the hot spot method. It should be noted that the S-N curves include the
tensile residual stresses present in the tested samples. Several experimental studies have confirmed
that the hot spot method provides accurate results in real case scenarios [9], [11].
The hot spot approach in FEA is widely used nowadays and is one of the methods which have
proven to provide results of acceptable accuracy. However, the main drawback of the hot spot
method is that it does not consider the local stress due to the weld itself resulting from the sharp
notch at the weld toe.
2.4.3.2 Through Thickness Stress Linearization
The linearization of stress through the thickness of the plate is required for certain cases to obtain
more accurate results. There are many different linearization techniques, but the one that is
commonly used is Through Thickness at Weld Toe (TTWT) [12]. The structural stress in this
method is calculated directly in the weld toe plate cross-section, as shown in Figure 10. When using
a coarse mesh, nodal averaging can cause stress underestimation. This method should thus only
use the elements present in front of the weld toe to avoid nodal averaging by the surrounding
elements [12].
13
Figure 10: Through thickness at weld toe method, redrawn from [12]
The stress distribution under the weld toe is non-linear, as depicted by the arrows inside the trend
in Figure 10. The non-linear stress distribution can be integrated to generate a linear distribution
from which the membrane and bending stress components can be found. It can be inferred from
Figure 11 that the local notch stress is the sum of bending, membrane, and non-linear stress. The
TTWT method does not capture the non-linear stress component caused by the notch, hence, the
structural stress will be the sum of membrane and bending stress [12].
Figure 11: Decomposition of local notch stress, recreated from [1]
There are a few more approaches for estimating the structural stress at the weld toe: Dong’s
approach, Xiao Yamada or 1mm method, and Equilibrium equivalent structural stress method, also
known as 𝐸 2 𝑆 2 (see Appendix D – Structural stress approaches for further scope). All these
methods consider thickness effects during weld fatigue assessment by using the stress distribution
in the thickness of the welded plate during the calculation of the structural stress. As a result, these
methods can give more accurate fatigue assessment than the hot spot method as the latter does not
consider the thickness effect [13].
2.4.3.3 Dong’s Structural Stress or Master S-N curve approach
Dong’s approach utilizes a procedure similar to TTWT to calculate structural stress but at a distance
𝛿 from the weld toe. Dong’s approach is claimed to be insensitive to mesh size and element type
as it takes the stress at a distance from the weld toe [14]. The claim has been proven numerically
for shell elements but is false for solid. This is because the approach fails to capture the effect of
shear forces acting in the lateral direction. Research shows its inability in the case of solid elements
14
through comparison studies but has also proven that for 𝛿=0.4t, the approach gives appropriate
results as the effect of shear stresses is minimal at that distance from the weld toe [14].
Figure 12: Structural stress according to Dong, redrawn from [14]
The structural stress for Dong’s approach has been calculated at 0.4t throughout this project. The
structural stress, 𝜎𝑆 , is obtained as the sum of bending and membrane stress distribution in the
weld plate cross section as shown in Figure 12. The membrane stress, 𝜎𝑚 , and the bending stress,
𝜎𝑏 , are found by using the equations given below. The membrane stress is found by integrating the
horizontal stress, 𝜎𝑥 , along the direction of thickness, 𝑦. This membrane stress is then plugged into
the second equation to find the corresponding bending stress [8].
𝜎𝑚 =
𝜎𝑚 ∙
1 𝑡
∫ 𝜎 (𝑦)𝑑𝑦
𝑡 0 𝑥
𝑡
𝑡
𝑡2
𝑡2
+ 𝜎𝑏 ∙ = ∫ 𝜎𝑥 (𝑦) ∙ 𝑦 𝑑𝑦 + 𝛿 ∫ 𝜏𝑥𝑦 (𝑦)𝑑𝑦
2
6
0
0
𝜎𝑆 = 𝜎𝑚 + 𝜎𝑏
Where 𝑡 is the thickness of the plate and 𝛿 is the distance from the weld toe. The structural stress
is then substituted into the formula given below to find the structural stress parameter, ∆𝑆𝑠 , which
can be used with the master S-N curve to find the fatigue life.
∆𝑆𝑠 = ∆𝜎𝑠 ∙ 𝑡
𝑚−2
2𝑚
1
∙ 𝐼(𝑟)−𝑚
It should be noted that the thickness correction, effect of loading mode and geometrical
discontinuities are already included in this formula. The variable 𝐼(𝑟) is a dimensionless function
of bending ratio, 𝑟, and varies with the loading mode of the model and the crack type. Two cases
are shown below: edge crack, load-controlled (a) and semi-elliptical crack, small detail (b) [8].
1
𝐼(𝑟)𝑚 = −0.0732𝑟 6 + 0.2132𝑟 5 − 0.2063𝑟 4 + 0.091𝑟 3 + 0.0193𝑟 2 − 0.014𝑟 + 1.102 (a)
1
𝐼(𝑟)𝑚 = 0.0011𝑟 6 + 0.0767𝑟 5 − 0.0998𝑟 4 + 0.0946𝑟 3 + 0.0221𝑟 2 + 0.014𝑟 + 1.2223 (b)
Here the bending ratio is given by the ratio of bending stress to the sum of bending and membrane
stress and 𝑚 is the exponent in Paris law. The function will be different for semi-elliptical cracks,
15
but only edge-type crack was considered in this project. However, one should note that the crack
is not modelled during the analysis.
2.4.3.4 Xiao and Yamada or 1mm approach
The “1 mm method” is another structural stress method that captures the thickness effect well.
This is an unconventional approach because the structural stress is calculated at 1mm below the
notch tip. This approach is motivated by the assumption that the fatigue crack propagation occurs
1mm below the weld toe. The stress taken 1mm below the weld toe is claimed to capture the
thickness and size effect, thereby avoiding the necessity for a thickness correction factor for weld
plates thicker than 25mm. It is preferred to use first-order finite elements to avoid stress gradients
[15], [13].
Figure 13: Structural stress according to Xiao & Yamada, redrawn from [15]
To capture the stress at 1mm depth with acceptable accuracy, the finite element model must have
fine mesh, which is one of the main drawbacks of this approach. The other drawback is that the
method is not applicable in cases where bending stress is dominant [13]. This method has been
shown to provide results in good agreement with experimental evaluations except in cases when
bending is dominant. However, the 1 mm method tends to underestimate the stress for thin plates
as 1mm point below the weld toe exists close to the neutral axis [15].
2.4.3.5 Modified Structural hot spot stress
According to [16], the stress concentration factor, 𝐾𝑠𝑎 , can be found using the following formula,
depending on the difference between weld leg length, 𝑙𝑤 , and half thickness of the base plate:
𝐾𝑠𝑎 = 1 +
𝜎𝑤
𝑙𝑤
𝑡
(1 − ) 𝑓𝑜𝑟 𝑙𝑤 ≤
𝜎𝑛
𝑡
2
𝐾𝑠𝑎 = 1 +
𝜎𝑤 𝑡
(
)
𝜎𝑛 4𝑙𝑤
𝑓𝑜𝑟 𝑙𝑤 ≥
𝑡
2
where 𝜎𝑤 is the weld stress and 𝜎𝑛 is the nominal stress. The results yield FAT 95 for throat
thickness a = 3 mm, and FAT 83 for a = 7 mm [16], [17]. This method claims a few desirable
properties for increase in flexibility of analysis:
•
•
•
•
Simple meshes with various mesh element types and sizes can be used.
Useful also when root cracks are included
Applicable with coarse solid, plane, or thin shell element models,
Thickness correction is not required with wide range of thickness applicability
16
The drawback of this method is that it is applicable only for two-sided fillet lap welds and the study
[16] warns the reader to use this method for other type of welds with caution as the stress
concentration formula might differ.
2.4.3.6 Force equivalent traction stress
The force equivalent traction stress method claims to be able to capture the stress distribution
through the thickness regardless of whether using a coarse or a fine mesh. This method combines
the application of both Hot spot method and Through thickness method by extracting traction
stress at the hot spot point 0.5t and 1.5t and extrapolating it to find the structural stress at the weld
toe.
The study [18] claims that the mesh dependency is minimized by using nodal forces to calculate
sectional force and moments. The formulas below show the summation of axial force and two
bending moments using nodal forces to find the traction stress, 𝑝 , acting on the section. The result
of the summation is shown in Figure 14.
Figure 14: Decomposition of force equivalent traction stress of a section, redrawn from [18]
𝑝̂1 =
∑ 𝑓𝑖
𝑝̂ 3 =
𝑙𝑡
+
∑ 𝑓𝑖
𝑙𝑡
6 ∑ 𝑧𝑖 𝑓𝑖
−
𝑙𝑡 2
−
6 ∑ 𝑧𝑖 𝑓𝑖
𝑙𝑡 2
6 ∑ 𝑦𝑖 𝑓 𝑖
+
𝑡𝑙2
; 𝑝̂ 2 =
6 ∑ 𝑦𝑖 𝑓 𝑖
𝑡𝑙2
; 𝑝̂4 =
∑ 𝑓𝑖
𝑙𝑡
∑ 𝑓𝑖
𝑙𝑡
6 ∑ 𝑧𝑖 𝑓𝑖
+
𝑙𝑡 2
−
6 ∑ 𝑧𝑖 𝑓𝑖
𝑙𝑡 2
+
−
6 ∑ 𝑦𝑖 𝑓 𝑖
𝑡𝑙2
;
6 ∑ 𝑦𝑖 𝑓 𝑖
𝑡𝑙2
Here 𝑙 is the length of an element, 𝑡 is the thickness of the plate, 𝑓𝑖 and 𝑝̂𝑖 is the nodal force and
traction stress at i-th node on the cut section and 𝑧𝑖 , 𝑦𝑖 are the z and y coordinate, respectively.
The traction stress from the cut section is multiplied with the shape functions for type of elements
used in the analysis. An example with bi-linear element is
1
1
1
1
𝑁1 (𝑟, 𝑠) = 4 (1 − 𝑟)(1 − 𝑠); 𝑁2 (𝑟, 𝑠) = 4 (1 + 𝑟)(1 − 𝑠);
𝑁3 (𝑟, 𝑠) = 4 (1 + 𝑟)(1 + 𝑠); 𝑁4 (𝑟, 𝑠) = 4 (1 − 𝑟)(1 + 𝑠)
where 𝑟 and 𝑠 are natural coordinates. The traction stress of the cut section is thus obtained as
4
𝑝(𝑟, 𝑠) = ∑ 𝑁𝑖 (𝑟, 𝑠)𝑝̂𝑖
𝑖=1
17
2.4.4
Effective notch stress approach
This approach is based on including stress raisers arising from geometrical discontinuities such as
notches, holes, weld defects, joints, etc. from the structural component which are usually not
captured by the methods discussed till now. It is necessary to include the stress due to local
geometry as it determines the realistic fatigue strength of the component based on the stress
concentration.
The basic concept of this method is to model the weld toe or root as a notch of radius 𝜌𝑓 which is
given by Neuber’s micro-support concept for welded joints as shown in Figure 15 where the
maximum principal stress is directly read from the FEA results of the local notch geometry [6].
This approach gives more accurate results compared to the structural stress methods as it gives a
much better representation of fatigue strength by including local geometry effects through the
reference radius or notch radius [19].
The modelling and pre-processing part for this method needs more effort than compared to other
methods. To capture the maximum stress, the model requires a higher element density in the notch
region. A complex geometry would require a sub model of the structure to concentrate only on the
critical location from where the stress should be extracted also resulting in reduction of
computational cost.
Figure 15: Notch rounding with reference radius, 𝜌𝑓 ; redrawn from [19]
The notch radius is usually set to 1mm for plates thicker than 5 mm and 0.05mm for thinner plates.
The notch radius for thin plates was proposed by Zhang, which is based on the relationship
between the stress intensity factor and the notch stress [6]. The element size in the notch region
should be in the range of 1/4th or 1/6th of the radius of the notch so, it is usually set at 0.25 mm.
The method gives non-conservative results for thin butt joints due to small stress concentration
occurring in such joints [20].
One of the main advantages of using this method is that only one Fatigue class curve is used
regardless of the geometry or loading detail. For steel welded joints, IIW recommends the FAT
18
225 curve which will be linked to maximum principal stress found from the analysis to find the
fatigue life. The disadvantage to this method is high computational time and meshing requirements.
2.5 Summary of approaches
Advantages
Nominal Stress approach
Simple, well known method
Simple and quick application with guidelines
Fatigue classes available
Disadvantages
Limited to simple geometrical changes
Less compatible and less accurate with
complex geometries
Only applicable for the tabulated structural
details
Hot Spot method
Most widely used
FE-modelling effort is less
Medium mesh requirements
Good accuracy
Less number of fatigue classes and S-N curves
Applicable for both shell and solid models
Through Thickness Linearization
Fatigue life calculations include thickness
effect
Good accuracy
Applicable in complex geometrical and loading
conditions
Intermediate mesh requirement
Dong’s Structural stress approach
Mesh independent
Good accuracy
One Master S-N curve
Xiao Yamada or “1 mm approach”
Post processing is simple
Good accuracy
Thickness effect included
Not applicable for weld root failure
Mesh dependent
Thickness effect is not included
Only applicable for the tabulated structural
details
FE-modelling needs more effort to capture
stress along thickness
Nodal averaging underestimates stress
Works only for solid model
Mesh dependency is observed when solid
elements are used
Works only for solid model
Fine mesh is required
Not applicable for bending stress dominant
cases
Works only for solid model
Modified structural stress approach
Mesh Independent
Best Accuracy
Applicable for all Thickness
Root crack scenario applicable
Force traction stress method
Promising improvement for Hot spot method
Good accuracy
Mesh insensitive
Thickness effect is included
Effective notch stress approach
Better accuracy than rest of the above
One S-N curve
Thickness effect is captured
Applicable for weld root failure
Not for every type of weld joint
Needs more research for stress concentration
on different types of weld joint types
Works only for solid model
Needs more research to prove applicability
Works only for solid model
More FE-modelling effort
Requires sub-modelling in case of less
computational capability
High mesh requirement
19
Section 2.5 presents the summary of all the methods in the form of a table, which has been
collectively obtained from the literature([1] – [25]).
The nominal stress, modified structural stress and force traction methods were decided not to
proceed with because the first two of them were not applicable in every type of weld joint and the
last one required more research for comparison and validation.
20
3 Finite element analysis
This Chapter describes the FEA done on three case studies with information about modelling, preprocessing steps, and results from postprocessing. Further comparison of results of some methods
from this project that were available in reference literature was done for validation.
3.1 Case study 1
The first case study concerns a geometry obtained from [21], shown in Figure 16. It is a simple
Transverse joint (T-joint) with an incomplete weld along the joint. The reference study [21]
contained an FEA on the model and a comparison between the fatigue life results from the nominal
stress, hot spot, and effective notch stress methods. In the reference study, a so-called coefficient
for risk of failure, 𝜑𝑄 , was included in the fatigue life calculation as shown in the formula (a) shown
below which is a formula to calculate the fatigue life from the hot spot stress method. A 50% failure
risk was considered in the reference study to match the fatigue life results obtained from FEA with
experimentally tested fatigue life. Different values of 𝜑𝑄 is shown in Table 1. The risk of failure
taken in this project is 2.3%, which makes 𝜑𝑄 = 1. This is done so that the results are comparable
with the results from the automatized process.
𝑁 = 2 ∙ 106 ∙ (
𝜑𝑄 ∙𝐹𝐴𝑇 𝑚
𝜎𝐻𝑆𝑆
) (a),
where FAT is the fatigue strength at 2 million cycle for a 97.7% survival probability S-N curve, 𝑚
is the slope of the S-N curve and 𝜎𝐻𝑆𝑆 is the hot spot stress obtained from FEA postprocessing.
Consequence of failure
Testing
Negligible
Less severe
Severe
Very severe
Approximated risk of failure
50%
2.3%
0.1%
0.01%
0.001%
Coefficient for risk of failure φQ
1.3
1.0
0.87
0.8
0.74
Table 1: Coefficient for risk of failure for different percentages of failure, referred from [21]
Figure 16: Dimensions of case study 1 geometry (in mm)
The geometry was modeled in Abaqus and the dimensions from the reference study [21] were used,
as shown in Figure 16. The quarter model of the geometry was used in the analysis as the geometry,
loading, and boundary conditions have symmetry as marked with the blue centerline in Figure 16.
The same material properties from the reference study [21] were applied with the isotropic elastic
properties shown along with Figure 17.
21
Material properties
𝐸 = 210 𝐺𝑃𝑎
𝜈 = 0.3
Figure 17: Meshing with tetrahedral elements
The model was meshed with quadratic tetrahedral elements, C3D10I, with improved surface stress
formulation, as shown in Figure 17. The model was partitioned to have the FE mesh nodes at the
points where stress must be extracted for all the methods. For example, the stress should be
extracted from the nodes at 0.4t, 0.9t, 1.0t, and 1.4t distance from weld toe for linear and quadratic
of hot spot method. The model should be partitioned on the thickness to extract stress 1 mm
below the weld toe for the 1 mm approach calculation.
The reference study [21] contained two cases based on how the weld was loaded. Case 1 was for
applying load in the base plate, making it a non-load carrying fillet weld, which is a type of weld
that contains an attachment plate which does not involve in transmitting load to the main or base
plate. Case 2 was for applying load in the attachment plate, making it a load-carrying weld. This
project only uses the loading case 1 from the study for analysis and comparison, as shown in Figure
18.
Figure 18: Loading case
Symmetry boundary conditions were used to constrain x- and z- direction where symmetry exists
in the geometry. The model in this project was given boundary conditions like the reference study,
where it represented the testing scenario as accurately as possible. A reference point was created at
the point shown in Figure 19 as RP-1. A reference point is a point you can create in a part or
assembly in Abaqus. It can be created anywhere in the space and is useful for creating a point where
there is no vertex available. A rigid body constraint is introduced to constrain the motion of the
points present in the highlighted surface in the expanded image, to the motion of the reference
point. This is used to apply a distributed load in Abaqus. A load of 100 kN is applied at the reference
point shown in Figure 19. This case study involves a pulsating load with stress ratio R = 0.
Therefore, the stress obtained from the FE results is directly plugged in the formula for calculating
fatigue life.
22
Figure 19: Boundary conditions of case study 1
3.1.1 Results
•
Hot spot stress
The stresses extracted from the predetermined distances are put in Table 2. This was done using
the probe values tool, available in the Abaqus query window.
Distance from weld toe
0.4t
0.9t
1.0t
1.4t
Maximum principal stress [MPa]
107.94
105.60
105.41
104.75
Table 2: Stress extracted from the model for hot spot stress calculation
The maximum stress values were extracted from the following path created in Abaqus by defining
a node list. The points shown in Figure 20 are in the order as given in the table.
Figure 20: Nodal points for stress extraction for the hot spot method
As mentioned in Section 2.4.2.1 Hot spot method, hot spot stress can be extrapolated in three ways:
Linear with coarse mesh, linear with fine mesh, and Quadratic. The linear with coarse mesh was
not implemented for this model as the mesh density is fine near the weld toe. The stress results
23
extracted from the points 0.4t and 1.0t will be used for Linear extrapolation with fine mesh and
results from points 0.4t, 0.9t, and 1.4t will be used for quadratic extrapolation. The fatigue strength
class, FAT, was taken as 100 and the fatigue life, N, was calculated and presented in Table 3. The
value of the FAT and the formula shown below are referred from the reference study [21] and can
be referred in the IIW recommendations [4] for a non-load carrying weld type.
𝐹𝐴𝑇 3
)
𝑁 = 2 ∗ 10 ∙ (
𝜎𝐻𝑆𝑆
6
Type of extrapolation
Linear
Quadratic
Hot spot stress σHSS [MPa]
109.64
110.88
Fatigue life N [cycles]
1517500
1470000
Table 3: Hot spot stress results for the case study 1 model
It was agreed that the results obtained from this hot spot method is acceptable as the value for hot
spot stress is the same as in reference study [21]. The only variation in results was found in fatigue
life as the coefficient 𝜑𝑄 was assumed to be 1 for this project.
•
Through Thickness at weld toe (TTWT) method
Figure 21: Stress extraction for Through thickness method
Figure 21 shows which stress are extracted for the linearization of stress through the thickness.
Here the initial crack length was assumed to be 1 mm. The longitudinal stress values were used to
extract 𝜎𝑚,1 and 𝜎𝑏,1 , the vertical stress values were used for 𝜎𝑚,2 and 𝜎𝑏,2 , and shear stress acting
on the plane was used to extract values for 𝜏1 and 𝜏2 . The crack length was taken as 𝑙 = 1 𝑚𝑚
and the thickness as 𝑡 = 1 𝑚𝑚. One should note that a crack was not modelled during the analysis
but was assumed to have propagated for calculation purposes.
𝐹 = 𝜎𝑚 ∙ 𝑙 ∙ 𝑡
𝑀 = 𝜎𝑏 ∙ 𝑡 ∙
𝑙2
6
𝑄 = 𝜏∙𝑙∙𝑡
𝜎𝑠 = 𝜎𝑚 + 𝜎𝑏 =
24
𝐹 6𝑀
+
𝑙𝑡 𝑙𝑡 2
The structural stress parameter is found using the formula given in Page 15 and is plugged into the
master S-N curve equation given in Page 8 to find the fatigue life. There is no FAT value required
in this case. The results are shown in Table 4.
𝜎𝑚,1
120.956
𝜎𝑚,2
17.677
𝜎𝑏,1
2.013
𝜎𝑏,2
5.15
𝜏1
-8.907
𝜏2
12.07
𝜎𝑠
93.267
Fatigue life, N
1790000
Table 4: Results from TTWT for case study 1 model
•
Xiao Yamada or 1 mm method
Figure 22: Xiao Yamada method with 0.5 mm element
This method is based on extracting the stress 1mm below the weld toe which is marked with a red
point in Figure 22. The fatigue life was calculated using the same formula shown in the hot spot
stress section in Page 24 but the stress taken from the red point was used. Element sizes of 1 mm
and 0.5 mm along the thickness were compared to check for stress underestimation and the results
are shown in Table 5.
Element
1 mm
0.5 mm
Maximum principal stress (MPa)
98.7131
100.185
Fatigue life
2080000
1988900
Table 5: Results from Xiao Yamada or 1 mm method for case study 1 model
•
Dong’s structural stress method
A similar procedure like in TTWT was followed except that the stresses were taken at 𝛿 = 0.4 t
where the effect of shear stress is minimal. The same force-moment equilibrium approach applied
in TTWT method was used to find the structural stress which was then applied to the master S-N
curve to find the fatigue life. The results are shown in Table 6.
25
109.766
-8.319
101.2317
1934300
Membrane stress, 𝜎𝑚 [MPa]
Bending stress, 𝜎𝑏 [MPa]
Structural stress, 𝜎𝑠 [MPa]
Fatigue life, N
Table 6: Results from Dong's approach for case study 1 model
•
Effective notch stress approach
The Effective notch stress method, ENS, requires the region of the notch to be meshed finely
enough to capture the notch stress accurately. To reduce the computational cost, the sub modelling
technique was incorporated as shown in Figure 23. The sub model boundary condition was applied
to the highlighted surfaces shown in Figure 24 and the number of nodes on the connecting region
of the global model and sub model was the same. The sub model boundary condition in Abaqus
transfers the displacement obtained from the analysis of a global model to the sub model and hence
there exists no symbol to represent the boundary conditions in Figure 24.
Figure 23: Global model and sub model for effective notch stress approach
Figure 24: Sub model boundary conditions
Figure 25: Meshing of the sub model
The element size around the notch region was kept at 0.25 mm which is 1/4th of the notch radius
1 mm. The local seeds in Abaqus are used to assign an edge in the geometry a specific element size
different than the global element size. This function was used to modify the mesh density near the
notch so that a dense mesh was generated in the notch. The resulting mesh is shown in Figure 25.
The model attributes were modified to read the results from the main model and apply it to the
sub-model boundary conditions so that the displacements are transferred to the sub-model.
26
The results from the analysis can be seen in Figure 26 where the maximum principal stress can be
directly read from the analysis. The stress can be used to calculate the fatigue life with FAT value
as 225 as shown in Table 7. This FAT value was referred from both IIW [4], and the reference
study [21], and is constant for all types of geometry and loading scenario unlike the hot spot
method. The formula for calculating fatigue life in this method is the same as in hot spot method
as shown in Page 24, but the stress used in the formula and the FAT value are different.
Figure 26: Maximum principal stress from the analysis
Maximum principal stress (MPa)
Fatigue life
223.2
2048800
Table 7: Results from Effective notch stress for case study 1 model
The results from the ENS and hot spot method shown in Table 8 were in close agreement with
the results from the reference study [21] where only these two methods were implemented in the
same geometry. ENS method was considered to provide the most accurate results as most of the
literature suggests. Therefore, the results from the rest of the methods were compared with ENS
and are represented as percentage of difference in Table 9.
Method
Hot spot (solid)
Linear
Quadratic
Effective notch stress
Project stress results
[MPa]
109.64
110.88
223.2
Reference paper
stress results [MPa]
110
111
217
Error (%)
0.3
0.1
2.7
Table 8: Comparison of results between project and reference [21] for case study 1
Method
Hot spot
Linear
Quadratic
TTWT
1 mm method
1 mm element
0.5 mm element
Dong’s
Effective notch stress
Structural stress [MPa]
Fatigue life
109.64
110.88
93.27
98.7131
100.185
101.231
223.2
1553000
1496000
1790000
2080000
1988900
1934300
2048800
Percentage of
difference (%)
24
27
12.6
-1.5
2.9
5.6
-
Table 9: Case study 1 results of methods with their percentage difference compared to the effective notch stress
27
Shell model
The weld geometry can be modelled using shell elements in several ways, one of which is modelling
the weld as an oblique shell element. The mid surface shell model was created as shown in Figure
27 where the dimensions vary with the plate thickness and the weld leg length 𝑙𝑤 .
Figure 27: Weld modelled as oblique shell elements
The resulting shell model of the case study is shown in Figure 28 for reference. The plate thickness
was assigned to the specific shell surface and the weld geometry. The material and boundary
conditions were also applied and analysed. The disadvantage of using this model will be the inability
to capture stress along the thickness of the plate. All the methods except the hot spot method
require the thickness of the model in the geometry, so therefore, only the hot spot method was
applicable for shell models.
Figure 28: Shell model of case study 1
The results of the shell model show differences from the solid model due to difference in stiffness
between solid and shell elements. The results from shell element model for the hot spot method
are shown in Table 10.
Method
Hot spot
Linear
Quadratic
Structural stress [MPa]
Fatigue life
104.94
110.88
1731000
1705000
Percentage of
difference (%)
15.51
16.78
Table 10: Shell model results for hot spot with the percentage difference compared to the effective notch stress
28
3.2
Case study 2
The second case study concerns a longitudinal stiffener welded to a test specimen shown in Figure
29 that is subjected to bending load. This model is taken from a research paper [22] where it was
tested using strain gauges to calculate the structural hot spot stress. Results from the experiment
were then compared with the hot spot stress obtained from numerical analysis.
The reference study [22] dealt with two types of load cases: tensile and bending load on the same
geometry. This project only considers the bending load scenario as tensile loading was already
treated in case study 1. A wider perspective can be obtained from this case study by involving
bending load with longitudinal welds, unlike case study 1, where it was tensile loading with
transverse weld.
Figure 29: Case study-2 geometry
The same methods that were applied in case study 1 were implemented in this case study as well.
This expands the existing research by comparing results from methods other than the hot spot
method to find if the structural stress values agree with the reference study [22]. It should be noted
that the fatigue life was calculated without including misalignment, thickness correction, or risk
factor like in case study 1. The fatigue class for this type of loading is FAT 90, and a survival
probability of 97.7% was assumed in the calculations.
The material property is the same as used in reference study [22], which is from ASTM mild steel
of grade A, with similar isotropic elastic properties as in the previous case study. The loading is a
three-point bending scenario where the load is applied at the bottom of the longitudinal weld, and
the ends of the test specimen are held, as shown in Figure 30.
Figure 30: Case study 2 three-point bending loading case
29
A kinematic coupling between a reference point (RP-1) and a line representing the midline of the
specimen (magenta line) at the bottom surface was created as shown in Figure 31. This coupling
constrains the motion of the nodes on the midline (coupling nodes) to the motion at the reference
point in the user defined degree of freedom. A load of 6.86 kN was applied at the reference point
in the positive y- direction and the coupling nodes on the midline were constrained only in the ydirection to avoid formation of unwanted stresses as a result of contraction. This is a pulsating load
with stress ratio R = 0. Therefore, the same procedures apply for the calculation of fatigue life as
in case study 1.
Figure 31: Kinematic coupling between reference point and the midline
The element type used in the analysis was hexahedral 20-node brick elements, C3D20R, with R
indicating reduced integration. This element type was used in the reference study [22] and is thus
also used here for comparison purposes.
3.2.1 Results
The procedure followed for all the methods is the same as presented in case study 1. The results
from the case study are presented in Table 11.
Method
Hot spot
Linear
Quadratic
TTWT
1 mm method
1 mm element
0.5 mm element
Dong’s
Effective notch stress
Structural stress [MPa]
Fatigue life
483.36
498.2
587.6
447.6
484.56
585.14
1291
12870
11790
12970
16260
12815
11820
10600
Percentage of
difference (%)
21.4
11.2
22.4
53.4
20.9
11.5
-
Table 11: Case study 2 results with percentage difference compared to the effective notch stress
The fatigue life values from the hot spot method and Dong’s method showed accurate results,
whereas the 1 mm method showed bad accuracy compared to the previous case study. This
inaccuracy from the 1 mm method agrees with the conclusions inferred from [13]. Figure 32 shows
the sub-model showing results for the effective notch stress method.
30
Figure 32: Effective notch results for case study 2
Method
Hot spot
Linear
Quadratic
Project stress results
[MPa]
483.36
498.2
Reference paper
stress results [MPa]
493.84
514.63
Error (%)
2.1
3.2
Table 12: Comparison of results between project and reference paper [22] for case study 2
The hot spot method gave results that were in close agreement to the results from the reference
study [22], as shown in Table 12. For the second case the shell model was not prepared as the
comparison was only made for a solid model.
3.3
Case study 3
The third case concerns a rectangular hollow section joint that was referred from the SAE FD&E
committees’ “Fatigue Challenge” with specifications shown in Figure 33. The model was studied
in [23] using another structural stress approach called the 𝐸 2 𝑆 2 method. The method gave results
close to experimental results.
Figure 33: Case study 3 geometrical details (in mm)
The material is A13R-RC7 steel with the same isotropic elastic properties as in the other case
studies. The loading is applied at the end of the 101.6 × 101.6 mm section through a rigid link
317.5 mm above the center of the 101.6 × 101.6 mm cross-section. This is achieved by giving a
31
rigid link constraint between the center point and the reference point, RP-2, as shown in Figure
34, and the center point is given kinematic coupling to the surface of the cross-section.
The surfaces shown in Figure 35 were fixed in all directions, and a load of 17.8 kN is applied at the
reference point RP-2 in the positive z-direction. However, in this case the type of loading is
alternating which makes the stress ratio R<0. Hence, the stress obtained from the FE results is
doubled when plugged in for fatigue life calculation.
Figure 34: Rigid link and kinematic coupling in the hollow section
Figure 35: Boundary conditions on the rectangular hollow section
The element type used in the analysis was hexahedral 20-node brick elements, C3D20R, with
reduced integration and quadratic wedge elements, C3D15, for the weld geometry.
3.3.1 Results
The possibility of using the hot spot method with quadratic extrapolation and Xiao Yamada with
a 0.5 mm element size was limited due to geometrical and computational limitations. The rest of
32
the methods that are possible for this geometry are performed and listed in Table 13. The hot spot
method using linear extrapolation was performed by creating a path using a node list, as shown in
Figure 36. The location of high hot spot stress is marked in a yellow square, which coincides with
the location of the damage from the experiments conducted in the reference study [23].
Figure 36: Path created using node list for hot spot linear extrapolation on case study 3
The main model and the sub model used in effective notch stress is shown in Figure 37. This is
concentrated at the area where the crack occurred in the reference study [23].
Figure 37: Main model and sub model for effective notch stress on case study 3
Figure 38: Results from effective notch stress for case study 3
33
Method
Structural stress [MPa]
Fatigue life
Linear
TTWT
Xiao Yamada
1 mm element
Dong’s
Effective notch stress
336
421.8
314
356.74
713
52720
60344
64601
61650
63116
Hot spot
Percentage of
difference (%)
16.47
4.39
-2.35
2.32
-
Table 13: Case study 3 results with percentage difference compared to the effective notch stress
Method
Effective notch stress
Project stress results
[MPa]
356.66
Reference paper
stress results [MPa]
360
Error (%)
0.92
Table 14: Comparison of results between project and reference paper [24] for case study 3
The results from effective notch stress of this project agreed with the results from another
reference study [24], in which the effective notch stress method was performed for the same
geometry. Comparison of the results are shown in Table 14. Therefore, the other methods were
compared with the effective notch stress and are represented as a percentage of difference. The
hot spot method, TTWT, and Dong’s method showed conservative results.
34
4 Observations and discussion
The results from the case studies were used to compare the weld fatigue assessment methods and
rank them based on selected key performance indexes, KPIs. This comparison directed the project
work towards the most suitable method to be implemented as a tool.
The first case study was a simple T-joint with the load applied in the transverse direction on a nonload carrying weld affected indirectly by the load, unlike a load-carrying weld, which is under the
direct influence of the load. This classified the first case study under Fatigue class 100 or FAT-100
curve, and Type A hot spot for hot spot approach. The same fatigue class was applied for the 1
mm method. The other methods included all geometrical and loading conditions in a single
classification.
For the first case, the effective notch stress result was taken as the reference fatigue life, which was
compared with other methods for accuracy. The quadratic hot spot method shows the conservative
result when compared to the linear hot spot, which was not expected. All other methods showed
increased accuracy compared to hot spot except for the 1 mm method with 1mm element size
where fatigue life was overestimated, as shown in Table 9. This suggested the necessity to use a
fine mesh of 0.5 mm or denser near the weld region for the 1 mm method. The shell model was
evaluated for hot spot method in this case to show that the method was applicable in both solid
and shell model.
The second case study was a bending load scenario with a Type A hot spot, which classified it as a
FAT-90 curve. It can be noted in Table 11 that all the methods overestimated the fatigue life when
compared to the results from the effective notch stress, unlike the previous case study. This is
because the bending stress dominates, which increases the bending ratio and affects the structural
stress obtained.
The 1 mm method however showed high variations from the results when the stress was taken
from the point marked in red shown in Figure 39. The results from the red point for 1mm and 0.5
mm element sizes are represented in Table 15, where fatigue life is compared with the result from
the ENS method. The crack was now assumed to propagate under the weld bead like a lamellar
tear so, the 1mm stress was taken in the point marked in yellow, which gives somewhat acceptable
results. This demonstrates the sensitivity of the Xiao Yamada method towards bending stress,
which agrees with the conclusions referred from [13].
Figure 39: Xiao Yamada or 1 mm stress method on case study 2
35
Iteration
Element
[mm]
1 (point marked in 1
red)
0.5
2 (point marked in 1
yellow)
0.5
size 1 mm
[MPa]
432.92
442.7
447.6
484.56
stress Fatigue life
17970
16805
16260
12815
Error (%)
69.52
58.5
53.4
20.9
Table 15: Xiao Yamada of case study 2 compared with effective notch stress
The Dong’s method showed mesh dependency when used in solid models as can be inferred from
many research papers ( [12], [14], [15], [19], and [21]) but has been shown to give acceptable results
at the distance of 0.4 times the thickness of the plate from the weld toe as shown in Table 16.
Case study 2
Distance from weld toe
Structural stress [MPa]
Fatigue life [cycles]
% difference from ENS
0.4*t
585.14
11820
11.6
0.9*t
559.12
13493
27.4
Table 16: Dong's method results comparison based on distance from the weld toe
Apart from the mesh dependency and need for partitioning the geometry before analysis, the
calculation involved during post-processing is cumbersome. These are some of the difficulties
associated with through-thickness approaches in addition to the lack of resources for comparison
of results, especially with the TTWT method. It was noticed that this method required an
assumption on the crack length formed in the direction of the thickness during the calculation to
arrive at a result. This can increase the time for analysis when there are multiple welds to be analysed
simultaneously and is difficult to automatize.
The third case study was a complex model with a curved weld attached to a curved surface. Hot
spot quadratic was not performed as the stress at 1.4 t from the weld toe cannot be extracted from
the curved surface due to difficulty in partitioning. Xiao Yamada with a 0.5mm element size was
not performed, because of computational limits. Through thickness methods, TTWT and Dong’s
approach showed a similar accuracy range as shown for previous case studies. The effective notch
stress result from this project was verified with the research study [24], which was used as the
reference fatigue life for comparison with other methods.
The above observations made from the case studies gave a clear view on the methods and made it
easier to differentiate them based on accuracy, computational time, post-processing time, and
robustness for an eventual ranking of methods based on these criteria.
For the case of computational time taken:
•
•
•
•
Hot spot method took the least amount of time out of all methods as the mesh density
required in the analysis was intermediate.
TTWT and Dong’s approach took equal amount of time as hot spot.
Xiao Yamada was time consuming when the mesh density was high. It was proven that
fine mesh was required for good results from the analysis.
Effective notch takes the most amount of time out of all methods because of the highdensity mesh present in the notch.
Pre- and Postprocessing time taken:
36
•
•
•
•
Hot spot method required partition in the surface where stress is extracted and assignment
of local seeds for the partition. Local seeds indicate the number of elements present on the
surface near the weld toe region. Pre-processing steps were not much time consuming.
Postprocessing was also not time consuming as it only took few calculation steps to get the
fatigue life value.
TTWT and Dong’s approach took medium amount of time at pre-processing as
partitioning over the thickness of the welded plate was required. Postprocessing involves
creation of local coordinate system based on the weld geometry and lots of calculations
which was time consuming.
Xiao Yamada required partitioning and mesh refinement near the weld toe but, it has the
least amount of postprocess of all the methods as the structural stress was directly read
from the viewport.
Effective notch stress method took the most amount of pre-processing time as it required
sub modelling in all the case studies and detailed partitioning and assigning of local seeds
for accurate results. Postprocessing did not take much time as it took one step of calculation
after obtaining maximum stress from the analysis results.
Accuracy of each method:
•
•
•
•
•
Hot spot method showed consistent accuracy and can be the most conservative approach
of all.
TTWT method also showed consistent accuracy but is sensitive to the assumed initial crack
growth length.
Dong’s approach showed varying accuracy determined by the distance from the weld toe
and is suggested to have 0.4 t from weld toe to ignore the effect of shear stress.
Xiao Yamada was second most accurate method of all but is sensitive to bending stress.
Effective notch stress method is assumed to give the most accurate results of all the
methods and is found to be sensitive with respect to the element size on and near the notch
region.
The average error percentage of each fatigue life prediction methods are presented in Table 17,
Method
Hot spot
Error range (%)
20.62
19.1
13.13
6.47
8.7
Linear
Quadratic
TTWT
Dong’s approach
Xiao Yamada
Table 17: Average percentage difference of each methods with effective notch stress method
The robustness or flexibility of the methods was highly prioritized as the implementation of a
method as a tool required the method to assess numerous welds of different types simultaneously.
The ease of implementation of the method as a tool also adds to the advantage. Flexibility and ease
of implementation of each method:
•
Hot spot method can be easily applicable to numerous welds as the computational time is
less and the minimum mesh size requirement is 0.4 t.
37
•
•
•
•
TTWT required partition for all the weld plates along thickness direction and creation of
local coordinate system based on weld orientation to the global axes which makes it tough
to be implemented as a tool.
Dong’s approach is limited by the dimensionless function of bending ratio, 𝐼(𝑟), as it
changes based on the loading mode. In addition to that, it also requires local coordinate
system which is tough to automatize.
Xiao Yamada is proven to be sensitive to bending stress which makes it less flexible.
Effective notch is easy to implement when one is talking about postprocessing only.
However, it required lots of pre-processing work which makes it tough to implement when
there are multiple welds.
Considering all the above observations and discussions regarding all the methods and their
respective advantages and disadvantages, it was decided to proceed with the hot spot method,
which is robust enough and gives acceptable accuracy.
The decision was made easy by implementing a scoring matrix where the methods were scored
against the criteria discussed above with weight functions assigned to the criteria. The methods
were rated on the scale of 1-5 for each of the criteria with 1 being the least and 5 being the highest
score for each criterion. The weighted score of methods for each criterion was obtained by
multiplying the weight functions with the rating and is summed up to obtain the total score for
each method. The methods were then ranked based on the scores. The scoring matrix can be found
in Appendix A – Method scoring matrix.
38
5 A plug-in tool for weld fatigue assessment
This Chapter describes the internal workflow in the developed tool for weld fatigue assessment. It
starts with a brief explanation of the user input requirements and the working to arrive at the result.
A summary of the workflow is represented as a flowchart in Appendix B – Workflow summary.
5.1
Introduction
There are currently several commercial tools available for fatigue evaluation of welds. These
software packages directly read the stresses from the numerical calculations. However, most of
these software packages do not come with an automated post-processing plug-in that is specific
for the fatigue evaluation of welds. Thus, there arises a need for a user interactive plug-in that is
easily accessible in Abaqus. The primary objective for this thesis has been to develop a tool that
can evaluate the fatigue life of multiple welds which makes it convenient for the user to automate
most of the steps in postprocessing.
The hot spot stress method was selected based on its ease of applicability for different loading,
geometrical, and model type scenarios. The computational time is also minimal for the hot spot
method. The combination of this method and the finite element method is widely employed in
postprocessing welded joints. The hot spot method can assess multiple welds simultaneously.
Hence, automatizing the process can reduce the postprocessing time by a significant amount.
The hot spot stress for a welded joint is obtained by extracting the principal stress acting on the
surface perpendicular to the weld. Usually, the surface is partitioned at the place where the stress
is read out at a predetermined distance from the weld toe. The stress is extracted manually for each
hot spot location and finally extrapolated using the formula given for that type of extrapolation.
This increases the time involved when there are multiple welds.
The plug-in tool was developed in Python by using functions from FOX GUI Toolkit and Abaqus
GUI Toolkit. The FEA software has an inbuilt Python library whose contents vary based on the
software’s version. However, it contains the NumPy library, which is very useful for building a tool
for postprocessing. The tool will act as an extension for postprocessing with extra procedures
where the user is required to provide some inputs about the welds, and the results will be plotted
according to the requirement.
A Plug-in tool is either built by using Really Simple GUI (RSG) Dialog Builder or by using the
GUI Toolkit manual, which involves coding the interface from scratch using Python. The RSG
Dialog Builder is an inbuilt Abaqus function used to create a dialog box that can connect an
interface to the commands written in the kernel. Building the tool using the RSG can make the
tool non-updatable based on the version. Hence, in this project the plug-in tool is built using the
Abaqus GUI Toolkit manual so that it is updatable for future needs.
5.2
User inputs
There are some basic user inputs required for the calculation of hot spot stresses for welded
joints. These inputs are defined by the user in the starting dialog box and are
•
•
•
Weld geometry, in this case, the weld toe edge
Face adjacent to the weld toe edge where stress is extracted
Hot spot stress extrapolation type: Type A and B
39
•
•
Fatigue class, design codes: FAT 90 and 100
Loading type: Pulsating (zero-max-zero) and alternating
The first input required is the weld, which is taken in the form of an edge. thereby making it usable
in cases where there is no weld geometry as well (shown in Figure 40). The user is essentially
selecting the weld toe where a hot spot exists, and to select multiple welds when the critical location
is unknown, the user must select the last edge of the current weld twice. This informs the program
to create a set and separate the weld, and to create a new set for the edges of the next weld.
Figure 40: Edges of weld in solid model with weld geometry and shell model with no weld geometry
This way of surveying the whole weld instead of assuming a spot is done so that the hot spot stress
trend can be calculated for the whole weld. It can help detect the location for a crack to occur,
which is not usually known during the design phase. The secondary input for edges of the weld is
the number of divisions on each weld. It can be given a zero if no division is required and is
assigned ten by default.
The stresses at the edge of the weld toe are calculated in one direction based on the selected face,
as shown in Figure 40. There can be only one face attached to all the edges of the weld, or each
edge might have a separate face attached so, the tool is made to check if the assigned face is attached
to the edge.
The next step is to select the type of hot spot and the corresponding type of extrapolation for that
hot spot. Type A and Type B hot spot can be selected in the first dialog box, and the interface
makes sure that option from both the types cannot be selected, which is necessary to avoid
semantic errors. The tool at the present state can look at a single type of hot spot weld at one
iteration but can be modified to look at different types of welds at the same iteration in the future.
Finally, the user must specify the fatigue class based on the geometry and loading of the model
being evaluated. Currently, the fatigue classes 100 and 90 are included, but more can be included
based on the model.
5.3
Methodology
The workflow of the fatigue assessment tool is,
•
•
Define the number of welds and their corresponding weld toe (edges) along with the
number of divisions on each weld’s edges
Determine type of weld geometry; straight weld, slant/oblique weld, and curved weld
40
•
•
•
•
5.3.1
Find the normal to the weld toe where the stress read out points exist
Calculate the coordinate points and create path for stress extraction
Extract stress and calculate fatigue life based on the extrapolation type and design code
with the given assumptions and delimitations (Heading 1.4).
Report results in plot with user inputs
Segregation and classification of welds
When the user inputs were provided in the first dialog box, the GUI command (AFXGuiCommand3)
transfers the object information to the kernel, where it will be used for further steps. The kernel
can be considered as the backbone of the tool as it connects all the functions and contains every
step from the beginning to the end.
As of the present state, the important inputs that the kernel receives from the command are the
edge object, which contains the information about all the edges of every welds combined, the face
object, which consists of all the faces selected. In addition to that, the inputs regarding the
extrapolation type, the fatigue design codes, and the loading type are also received by the kernel.
The edge object has all the information about the edges selected, which can be accessed by the
index number. By using the index number, we obtain the vertices of the edge, which directly gives
the coordinates of the weld edge.
-------------------------------------------------------------Import modules
Start function Hoteval
Get edge object myEdge from AFXGuiCommand
IF length of myEdge > 1 THEN
FOR i in 1 to length of myEdge
Get vertices of current edge
Get coordinates of the vertices
Append into variable Welds at position [t][k]
Add k by 1
IF myEdge index == previous myEdge index
Add t by 1
Append empty array to variable Welds
Position K is zero
End of If statement
End of For loop
Do Coordcheck
Do Postproc_multi
Elif length of edge object == 0
Do Postproc
End of If statement
--------------------------------------------------------------
This Pseudo code snippet shows how the program will segregate welds by checking if an edge is
selected twice. It should be noted that the DO keyword in the code means to perform a function
calling action.
A code in its developing stages is expected to have few bugs or flaws in the functioning, and this
tool had one that was found at the early stages. It was related to the numbering of vertices of an
edge in Abaqus. The FEA software has a convention of assigning a parameter to each edge, which
3
Abaqus GUI Toolkit Reference Manual
41
increases from 0 to 1 from one end to the other. This affects the order in which the user can choose
the edges as the path is created based on the coordinates of the vertices from the selected edge.
Figure 41 shows two examples of how a path is created when the user selects the edges of a weld
in two different orders. The user is selecting the edges in the anti-clockwise direction in the lefthand side of the picture, which coincides with the parameterization of the vertices from 0 to 1 so
the path is created without any discrepancies. Whereas, in the second case (right-hand side), the
user selects it in the clockwise direction, which does not coincide with the ascending order of
parameterization of the vertices. Therefore, the path starts from the 0th vertex of the smaller edge
and abruptly extends to the 0th vertex of the longer edge and ends at the same point.
Figure 41: Path creation based on order of edge selection
This problem was solved by using the function Coordcheck, which can check the order of the
parametrization of the vertices of an edge and will arrange the vertices in the order of the user’s
selection to avoid the discrepancy. The function also removes the redundant vertex of the
consecutive adjacent edge. This makes the tool insensitive to the order in which the user selects
the edges of a weld, thereby making it more flexible.
5.3.2
Determination of type of weld geometry
After the weld segregation and classification, the post-process function is performed where the
first step is to determine the type of weld geometry. The weld geometry types are differentiated
based on whether the weld edge is straight, curved, or oblique. This is determined and then sent to
another function called Path Creator, which then creates the coordinates for the welds and sends
it in the form of a list for the creation of path.
It should be noted that the limitations of the tool at the present state would be its incapability to
extract stress from a weld lying on a curved surface. This problem can be overcome by projecting
the points onto the surface but requires more time to research the issue. Although the tool is
applicable for the weld geometries mentioned before, it still must be applicable for spline, which
requires more time and study of Bezier curves, control points, and so on.
5.3.2.1
Straight welds
The weld toe is defined by the edge selected and as mentioned before, the tool takes the coordinates
of the vertices present on the edge to the next steps. This is necessary to create a path that requires
42
the start and endpoint coordinates along with the distance from the weld toe and the type of weld
as inputs.
For the first case, which is a straight weld, the vertices coordinate values for a single axis are
supposed to be unequal while the other axes’ values are equal. The program checks for the presence
of a curve or radius by using a software library keyword called getRadius4, which returns the
radius of the edge object in case it is curved. Whenever the weld toe edge is straight, an exception
error is passed by the exception handler (try-except loop from Python) to set the variable to zero
as there is no radius.
-------------------------------------------------------------Import Pathcreate function as pc
Start function Postproc/postproc_multi
Get coordinates of vertices, radius and face object
Get normal of face object set it to variable gi
Assign to (x1, y1, z1) and (x2, y2, z2)
If radius == 0
If x1 != x2 and y1 == y2 and z1 == z2
If check for y/z normal gi[1/2] is 1 or -1
Set norm as 0/1
Do pc.pathcreatex
...
Check similar If conditions for y and z axis
Do pc.pathcreatey or pc.pathcreatez with norm as 0/1
...
--------------------------------------------------------------
The pseudo-code snippet presents how a straight weld is handled by the program to create the
path. The normal of a selected face which is attached to a weld is obtained by using a software
library keyword called getNormal5, which is specifically for a face object keyword. The normal of
the attached face is checked, and the program will set the variable norm as 0 or 1 based on the
normal direction. This will affect how the path is created by providing the direction at which the
distance from the weld toe will be offset.
Figure 42: Path creation for a quadratic extrapolation of straight weld
4
5
Abaqus Scripting Reference Manual
Abaqus Scripting Reference Manual
43
Figure 42 shows an example of a straight weld that lies on one axis (y-axis) and is perpendicular to
the rest. Here, the coordinate value for the y-axis of points 1 and 2 will not be equal whereas, the
rest will be equal, this will satisfy one of the three if conditions. The normal for the attached face
will be in z-direction which means that the variable gi[2]6 will hold the value 1. This will assign a
value of 1 to the norm and the path is offset to predetermined distances in the x-axis.
5.3.2.2
Slant or Oblique welds
The previous approach cannot be used when the weld toe propagates in a 2-d direction i.e., the
weld toe line lies in the x-z plane but only perpendicular to the y-axis, as shown in Figure 43. This
requires the code to call another function where the corresponding calculation are made to find
the start point, endpoint with the slope of the line, and so on.
Figure 43 : Geometry example for a slanting weld without the weld geometry
The geometry in Figure 43 can be taken as an example for a slant weld where the coordinates of
points 1 and 2 are known. The y-axis coordinate value for the points will be equal while the rest
will not be. This will call a function to create a path in the x-, z- plane with the coordinates and the
distance from the weld toe as the input as the rest of all things required to trace the path are
calculated.
The first step of calculation when a line is slant is finding the slope, which in this case is:
𝑠𝑙𝑜𝑝𝑒, 𝑚 =
𝑧2 − 𝑧1
𝑥2 − 𝑥1
The equation of line is formed with the slope and the constant c which can be found by substituting
the z and x values into the equation and solving for c
𝑧 = 𝑚𝑥 + 𝑐
The first objective is to find the coordinates of the starting point of the offset line of distance, 𝑑 =
𝑛 ∗ 𝑡 where t is the thickness of the weld plate and n is the pre-set distance from the weld toe. To
gi is returned in the form of (x,y,z) with values ranging from -1 to 1; gi[2] refers to the index position of z value in
the array (0,1,2)
6
44
find the coordinates, we need the equation of the line perpendicular to the current line which can
be done as follows
𝑧 − 𝑧2 = −
1
(𝑥 − 𝑥2 )
𝑚
And use the distance formula or the equation of circle to form another equation
(𝑥 − 𝑥2 )2 + (𝑧 − 𝑧2 )2 = 𝑑 2
Now that there are two equations with two variables, it can be solved for x and z
(𝑥 − 𝑥2
)2
(1 +
2
1
+ (− (𝑥 − 𝑥2 )) = 𝑑 2
𝑚
1
) (𝑥 − 𝑥2 )2 = 𝑑 2
𝑚2
𝑥 = 𝑥2 ± √
𝑑2
1+
1
𝑚2
The value of z can be found by plugging in the value of the x in the line equation and solving for
z. Repeating the same steps will give the start point and the endpoint of the offset line of the same
slope of the distance, d, from the weld toe. Now, the offset line can be traced by using the line
equation and the available x values of the offset line. The expected output from the code for a
linear type of extrapolation can be seen.
Figure 44: Path creation for a linear extrapolation of a slant/oblique weld
This path creation shown in Figure 44 is for a linear type extrapolation for a Type A weld where
only two distances from the weld toe are considered and also are divided into 10 equally distanced
points.
45
5.3.2.3 Curved welds
A weld in form of a circular curve presents itself with more challenges as both previous algorithms
are not applicable. The first thing to know about a curve would be its origin or centre coordinates,
which are usually found by solving a couple of equations. The inbuilt software library keyword can
provide the coordinates of the two endpoints of the circular curve, the radius, and the
circumference. Although this seems to be a situation where the values can be easily plugged into
an equation to find the centre, the Python library for Abaqus does not contain all the necessary
libraries for certain functions i.e., one cannot plot separately using Python libraries such as
Matplotlib and SciPy. Depending on the version of the Abaqus, the libraries present in the inbuilt
Python varies along with the Python version.
This appears as a limitation for several upcoming processes but for this case, it would be the
disability of using symbols for solving equations. The process of solving complex equations with
two or more variables required the usage of symbols, and this posed as a challenge as the current
Python version was not able to use symbols in all the versions of Abaqus except for the recent
version7. Keeping the motive of developing a robust tool that is applicable in all versions, the
problem was taken differently, and the centre of the curve was found using just the two endpoint
coordinates and the radius of the curve.
Taking the same geometry used in the previous Section as an example, the coordinates of points 1
and 2 in Figure 45 are known, along with the radius of the curve and the circumference. The code
checks for the radius and sends the user inputs, radius, and the coordinates of the end points to a
function where the calculations occur.
Figure 45: Geometry example of a curved weld without weld geometry
Let the coordinates of the point 1 be (𝑥1 , 𝑧1 ), point 2 (𝑥2 , 𝑧2 ) and the centre of the arc, (𝑥0 , 𝑧0 ).
The chord connecting the point 1 and 2 is perpendicular to the bisector from the centre of the arc.
So, by using the point-slope formula and distance formula and solving for the centre coordinates,
we can arrive at the solution. A brief derivation of the problem is shown for reference.
Slope of the line connecting 1 and 2 (line1-2) is
7
𝑧2 −𝑧1
𝑥2 −𝑥1
3DS SIMULA Abaqus 2020
46
and the perpendicular slope is
𝑥1 −𝑥2
𝑧2 −𝑧1
.
The midpoint of the line 1-2 is given by the midpoint formula (
𝑥1 +𝑥2 𝑧1 +𝑧2
2
,
2
).
The midpoint of line 1-2 and the centre of the arc makes a line and the equation for this line can
be found using point-slope formula.
𝑧0 −
𝑧1 + 𝑧2 𝑥1 − 𝑥2
𝑥1 + 𝑥2
(𝑥0 −
)
=
2
𝑧2 − 𝑧1
2
As the chord connecting points 1 and 2 and the bisector from the centre of the arc, o, creates a
right-angle triangle as shown in Figure 45, using trigonometry one can arrive at the solution,
tan (
|𝜃 − 𝜋|
2𝑟𝐿
)=
2
𝑙
where 𝑟𝐿 is the distance of the centre from the midpoint of the line 1-2, 𝑙 is the length of the line
connecting points 1 and 2 and 𝜃 is the angle formed by the two arc endpoints as shown in Figure
45.
The distance between the centre of the circle and the midpoint is given by
𝑟𝐿 = √(𝑥0 −
𝑥1 + 𝑥2 2
𝑧1 + 𝑧2 2
) + (𝑧0 −
)
2
2
By substituting 𝑧0 from the point-slope formula and solving for 𝑥0 , the formulas for finding the
coordinates of a centre of arc using the end points of an arc and radius was found.
𝑥0 =
𝑥1 + 𝑥2
𝑧1 + 𝑧2
𝜃−𝜋
)
±
tan (
2
2
2
𝑦0 =
𝑧1 + 𝑧2
𝑥2 − 𝑥1
𝜃−𝜋
)
±
tan (
2
2
2
After finding the centre of the arc, the starting degree of the arc or the position of point 1 in the
polar coordinate system is found. This gives the starting degree value for the rest of the offset lines.
The total degree of rotation can be obtained from the circumference data, and the divisions are
made on the span of the total rotation in degrees. Figure 46 shows the result of the code with the
curve offset by 0.4t from the weld toe.
Figure 46: Path formation for a curved weld without weld geometry
47
5.3.3
Extraction of stresses
The hot spot stress at the weld toe is found by extrapolating the stresses from the pre-set distances
from the weld toe. Some loss in accuracy can be expected due to nodal averaging and extrapolation
of the nodal stresses. However, the results can be appropriate when the mesh applied is fine
enough. It should be noted that when creating the path using point list, the path is independent of
the mesh formation on the surface and lies fixed in a space irrespective of changes in the model.
So, to avoid errors, only the undeformed model was used while extracting results from the path.
While extracting the stress from the specified path, the required inputs are the points from the
path, a variable indicating the type of results that is to be extracted, which in our case is the max
principal stress, and finally, the type of model output shape, which is undeformed. This changes
slightly when the shell model is evaluated as one needs to specify which normal of the surface is to
be considered for stress extraction. The user is asked to give input regarding the normal for
extraction.
The distinction between solid and shell elements are made automatically by checking the element
type. If the element type is ‘C’ it means continuum stress/displacement element in Abaqus, which
is usually used in three-dimensional solid models, whereas if it is element type ‘S’ then it is a
conventional or continuum shell model which is for displacement or stress calculation in a twodimensional or three-dimensional shell model.
Finally, after obtaining the stress results from the path as x-y data, based on the selected fatigue
design class and the extrapolation type the results are calculated and stored as x-y data with respect
to true distance. All hot spot stress values and fatigue values of each point at the weld toe are stored
and are visible from the postprocessor. Modification can be made to be able to segregate the data
to store as a text file in the future.
5.3.4
Reporting the results as plot
The user is given the flexibility to produce several plots in the post-processor module. The results
on hot spot stress along weld lines and the fatigue life along the weld line can be plotted. Although
the fatigue life and stress can be plotted for separate welds, the incapability to create a good
comparison of the fatigue lives of all the welds as bar plots in the same viewport was considered
as a limitation of the Abaqus solver. This was tackled by externally calling Microsoft Excel from
the program.
Microsoft Excel is called from the kernel code after storing the fatigue life of all the welds in a
separate variable, which can be sent to excel to be plotted as a bar plot. This is achieved in Python
by using a library called win32com, which can call Microsoft applications available in the working
environment. It is an obvious requirement for the working environment to have Microsoft Excel,
which is checked and is given the warning to ensure if it is installed in case of its unavailability. This
is required in the case of multiple welds to get the bar plots of fatigue life of all the welds as a
comparison.
48
6 Results and comparison study
The case studies were evaluated for hot spot stress using different choices of extrapolation, fatigue
design classes, and mesh sizes using the tool to compare the manual and automatized process of
evaluation.
6.1
Case study 1
The geometry was tested with different extrapolation types and mesh types for determining the
level of accuracy of the tool under different extrapolation types and to check the mesh
independence, which in turn determines the robustness of the tool.
Case study 1 is a Type A hot spot and, therefore, can be applied with three types of extrapolation:
Linear with coarse mesh, Linear with fine mesh, and quadratic. The results for both manual and
automatized were obtained for a 0.1*t mesh size and the element type being tetrahedral.
Extrapolation type
Linear with coarse mesh
Linear with fine mesh
Quadratic
Manual
1620140
1517500
1470000
Automatized
1620534
1529985
1450797
Error %
2.4e-4
0.0082
0.013
Table 18: Comparison of fatigue life from manual and automatized process for case study 1
It can be seen in Table 18 that the results from the automatized process agree well with the manual
extrapolation techniques even though the path has been created based on the input coordinates
and doesn’t necessarily coincide with the mesh nodes. However, it must be checked on how the
mesh size influences the results and how much variance it causes, which might give a limitation on
the tool. Hence, five sizes of mesh were tested using the automatized process including a manual
extrapolation from 10 points on a 0.1*t mesh size to check the accuracy of the results.
Figure 47: Mesh sensitivity analysis with different element sizes obtained from case study 1
49
The graph in Figure 47 shows how the mesh size affects the results obtained from the analysis. It
can be noted that the results start to converge at 0.4*t, which is the suggested mesh size for a hot
spot evaluation by IIW [4]. The red square markers on the graph represent the location of the
lowest fatigue life because of the high hot spot stress value obtained in the respective element size
iteration. This seems to shift location on the 0.5*t iteration suggesting inaccuracy. It should be
noted that the hot spot stress comparison graph is the exact mirror of the fatigue life graph in the
x-axis perspective.
Figure 48: Result plot annotation with weld detail and fatigue life in case study – 1
The result for a quadratic extrapolation of the case study with 0.1*t mesh size is shown in Figure
48. Annotation of the weld detail with fatigue life at that point is given in the viewport to show the
point of high hot spot stress, which suggests the possible point of crack propagation. This is helpful
when there are multiple edges on a weld.
6.2
Case Study 2
The first case study gave us the necessary knowledge for conducting a reasonable evaluation for a
single weld with one weld edge, whereas this case study will extend that knowledge to applying for
cases with multiple edges on a single weld and applying for different types of hot spots. The hot
spot stress from manual and automatized processes for single weld toe considered for the manual
was validated at the start.
The analysis results were obtained with hexahedral brick elements, and only the edge where the
manual results were taken was evaluated using the tool as a weld with a single weld toe. The results
for three extrapolation types were taken and compared with the manual extrapolation results in
Table 19.
50
Extrapolation type
Linear with coarse mesh
Linear with fine mesh
Quadratic
Manual
14220
12870
11790
Automatized
12423
11172
9974
Error %
0.126
0.131
0.154
Table 19: Comparison of fatigue life from manual and automatized process for case study 2
The next evaluation was done for a single weld with multiple weld toe edges using quadratic
extrapolation for which the continuous path was created as shown in Figure 49. This evaluation
gave us a thorough perspective of the welds. It can be seen in the figure that the annotation is on
the same side of the weld toe that was evaluated on the previous iteration with single edge criteria,
which suggests an overall evaluation of the weld geometry is preferred for a reasonable output
from the assessment.
Figure 49: Continuous path creation for multiple weld edges and fatigue life details
The final evaluation for this model was for the Type B hot spots at the top of the weld as marked
by red lines in Figure 50. The evaluation was done for fine and coarse mesh and compared in Table
20.
Figure 50: Type B welds in the case study 2 weld geometry
Extrapolation type
Coarse mesh
Fine mesh
Manual
37540
47843
Automatized
37447
47156
Error %
0.002
0.014
Table 20: Difference between results from automatized and manual Type B hot spot evaluation in case study 2
51
The evaluation of this case study gave a proof that the tool can work for welds with multiple
edges/weld toes and for a Type B hotspot meshed coarsely or finely. The tool in its current state
can calculate the fatigue life for a weld or multiple welds belonging to a single type of hot spot. The
freedom of choosing a different type of hot spot for different welds in the same iteration must be
included in the future for certain cases.
6.3
Case study 3
The complexity of weld geometry in this case study will help determine if the tool is robust enough
to evaluate welds with both straight and curved edge geometry. The analysis was carried out with
the same elemental properties except for some refinement near the weld area as the tool shows
acceptable accuracy with 0.3*t or smaller element size.
The original geometry that was analysed in Section 3.3 was not applicable for evaluation because
of the limitation of the tool not being able to create a path on a curved surface. However, with
future modifications and improvements, this problem might be overcome by projecting the path
points onto the surface. For now, the existing geometry was modified by extending the flat surface
such that stress readout points are accessible by the tool. The first iteration was just for the weld
shown in Figure 51.
Figure 51: First iteration of case study 3 using the tool. Weld_1_path_04 is shown in the figure
In the results, a shift in the position of high hot spot stress when compared to what was obtained
in Section 3.3 is seen as shown in Figure 51 with the annotation and arrow. The point of high stress
was expected to be in the region of top curved weld marked with a yellow rectangle as suggested
by the reference study but, due to the geometrical changes, has shifted to the top corner of the
weld.
To compare with the manual linear extrapolation method applied to the original geometry, a linear
extrapolation was implemented with the tool on the modified geometry. The results obtained from
both manual and automatized in the yellow rectangle region is presented in Table 21. It should be
noted that the comparison, in this case, is done between the original geometry used in Section 3.3
and the modified geometry, but the difference is less.
52
Type
Manual (original geometry)
Automatized (modified geometry)
Fatigue life (cycles)
52720
53850
Table 21: Comparison of results from manual and automatized process for case study 3
Figure 52: Hot spot stress comparison between automatized and manual extraction
The graph in Figure 52 shows the comparison of linear extrapolation from manual and automatized
in the modified geometry where the stress peak obtained in the top weld. The graph in Figure 53
is a comparison of the fatigue.
Figure 53: Fatigue life comparison between automatized and reference method
The next iteration was done for both welds on the geometry and the results are obtained, as shown
in Figure 54. An option to choose between stress and fatigue plots in the post-processing
visualization module was added. The tool showed that it works for a curved weld and can handle
multiple welds with ease. The amount of work done for a hot spot evaluation during postprocessing was substantially reduced by using the tool automatization.
53
Figure 54: Second iteration with evaluation of both welds
When there are multiple welds during an evaluation, the tool automatically gives a comparison of
the fatigue life of all the welds as a bar plot in Excel. Figure 55 shows the bar plot automatically
plotted at the last step of the evaluation using the tool. This can be used to check which welds go
beneath a certain amount of expected fatigue life and can give an overall perspective of the model.
Fatigue Life
Welds Fatigue Life Comparison Chart
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
Series1
l1
r1
Weld number
Figure 55: Welds comparative chart for case study 3
54
7 Conclusions and summary
Several conclusions were drawn from the theory and FEA and are presented in this report. A
summary of points highlighted during the making of the plug-in tool is also included.
7.1 Conclusions – Theory
The theoretical study on fatigue assessment of welds gave a wide variety of methods to examine
and understand the procedures involved in them to arrive at the results. This preliminary
comparison revealed several important points that helped filter the methods before moving on to
the next step. The Nominal stress method was eliminated first because of its incapability to work
with complex geometries and loading conditions.
Structural stress methods, SS, are continuously improving and are highly considered when FEM is
involved because of their capability to work with complex geometries. These methods consider
membrane and bending stresses eliminating the non-linear peak stress. This results in a relatively
less realistic fatigue strength value. In addition to that, most of these methods are applied only for
a failure occurring at the weld toe. The SS methods applicable for failure at weld root are reserved
for future work as it requires more research.
The study concluded that the effective notch stress method, ENS, gave the most accurate results
of all the methods according to several papers. This method takes the stress raiser due to the local
notch into account, unlike the SS methods. Regardless of the geometry or loading conditions, the
ENS method requires only one S-N curve. These are some of the desirable properties of the
method.
7.2 Conclusions – FEA
Three case studies were selected from the literature for the implementation of the methods. The
process of implementation gave a basic understanding of the procedures involved in each of them.
The results and the trend observed from these methods during analysis coincided with their
corresponding theory from reference papers. This part of the project resulted in the ranking of
methods based on selected criteria or key performance indexes, KPIs.
The hot spot method showed sensitivity towards the mesh size near the vicinity of weld toe. It
gave good results when the mesh was very fine (<0.4*t). Fatigue classes are available for all types
of geometries and loadings, and there were no difficulties faced while finding one for the selected
case studies. An average error of 19% was observed for the hot spot method when compared with
results from ENS, which was assumed to give the most accurate results out of all methods.
The methods TTWT and Dongs gave results with good accuracy for all the case studies. The results
are mesh-sensitive for solid elements but are appropriate at 0.4 t from the weld toe, which agrees
with [14]. When the weld was inclined at an angle to the global coordinate system, the local
coordinate system was used to obtain stress normal to the cross-section. Both methods consider
the thickness effect very well and require only one master S-N curve, unlike the hot spot method.
The 1 mm method gave good results only when there was tensile loading and showed high
deviations when bending stress is dominant, thereby agreeing with the conclusions in [13]. It also
required high mesh density in the vicinity of the weld toe, which increased computation time based
55
on the weld geometry. The postprocessing time was less as the structural stress is obtained directly
from the viewport.
ENS method gave an accurate and conservative fatigue life values for all the case studies. The
analysis results from this project for case studies 1 and 3 agreed with the results from the reference
paper [21] and [24]. This gave the results from this project credibility and when combined with the
conclusion from theory, it bolstered the decision of using the results from this method as the
reference value for comparing with other methods.
The FEA concluded with hot spot method being selected as the method to move forward with for
implementation as the plug-in tool. The reasons for that are:
•
•
•
•
•
•
Applicable for both solid and shell models.
Multiple welds can be considered simultaneously because of low computational time
Easy pre-processing and post-processing as it required less partitioning during the former
and as stresses can be read directly from the results in the latter.
FAT classes are available for all geometries and loading conditions
No need for assuming critical spot as the whole weld can be evaluated
No need for sub modelling or creating local coordinate system
The hot spot method gave less accurate fatigue life values compared to other methods but was
consistent in accuracy for all cases. This trade-off between accuracy and computational time/effort
was found to be inevitable but, the collective compromise involved in the hot spot method was
relatively low, which was the motivation behind the conclusion derived from the points.
7.3 Summary – Plug-in tool for weld fatigue assessment
The project resulted in a fully developed GUI- plugin tool capable of handling multiple welds in a
detailed manner with various options and flexibility given to the user. The fatigue assessment tool
is currently written using Python for Abaqus and enables fatigue assessment based on design codes
from IIW recommendation.
This tool for fatigue life assessment is an advanced add-on for post-processing that is capable of
substantially reducing the workload, time taken, and can be extended to further capabilities based
on the necessity. It is capable of assessing a single weld with the capability to give a detailed stress
trend throughout the weld length to assessing multiple welds in the same manner with an additional
comparison of fatigue life of all the welds as an Excel sheet chart. It is applicable for both shell and
solid models for any shape of weld geometry regardless of the orientation of it to the global
coordinate axis but only with a limitation of applicability for welds attached to a flat surface.
One of the main goals of this project was to build a plugin GUI that can be updated and changed
in the future, which can suit specific requirements of a project. Building the interface from the
scratch gave a clear idea of how the software connects the interface to the kernel code where the
calculations happen. This can be used by any engineer with basic knowledge in Python and Abaqus
classes while trying to modify the code to develop a plug-in for a similar method or while updating
the existing code. This program can act as the base for building a more robust tool applicable for
all kinds of welds on all surfaces and to make it assess fatigue due to failure at the weld root.
Summary from the analysis of the case studies,
56
•
•
•
•
•
Mesh dependency was not totally out of the equation. There was a minimum mesh size
requirement near the weld for acceptable accuracy. However, partitioning the surface
according to the extrapolation type was not necessary.
The tool can handle straight welds oriented parallel to single axis, oblique welds inclined at
an angle to two global axes and circular curved welds perpendicular to a single global axis.
This implies one limitation, namely that, the weld should be lying in a flat surface.
To get a good representation of stress trend along the weld, the provision of giving
divisions on each edge of weld was included.
Applicable to both Type A and B Hot spot welds but only single type of welds can be
evaluated together.
To represent the critical spot on a weld, the highest hot spot stress location is marked by
using an arrow and an annotation.
This plug-in can be made more robust and more automatized with updates and has the
potential to increase work-flow efficiency in a substantial manner.
57
8 Recommendations
The execution of the tool on the case studies gave a clear idea of what was missed out while building
the tool and what could be modified to obtain better results and make work-flow easier. Some bugs
or flaws exist in a newly built tool, which can be optimized in several ways. But due to limited
experience in the language and limited time, the optimization process was skipped. With more
analysis on different types of models and geometries, one can search for errors within the tool.
This can be solved easily as the code is built clearly with separate functions for different aspects
making it clear where the error might be present.
But with regards to general functionality some of the possible improvements for the tool would
be,
•
•
•
•
•
•
•
•
To be able to extract stresses from a curved and oblique surface getting it one step closer
to a robust tool
More fatigue design codes from different recommendations can be included for various
industrial applications
Multiaxial stress states should be included for evaluation of complex structures
To be able to evaluate different types of hot spots simultaneously.
Decrease the number of user inputs in between the first dialog box and the results
reporting; to automatize all the possible processes.
To be able to find the normal for a curved or slant weld automatically.
To make it applicable for more types of welds geometries i.e., spline
The tool should be able to find which normal of a shell surface to extract stress from,
automatically.
Further research on other methods and all the scope for developments will results in a much
more efficient, robust, and advanced tool capable of providing results with improved accuracy.
58
References
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[3] W. Fricke, “Recent developments and future challenges in fatigue strength assessment of
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Engineering Science, 229(7),, vol. 229, no. 7, 2015.
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[5] J. Schijve, Fatigue of Structures and Materials, Springer, Dordrecht, 2009.
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[10] H. Erwin and O. Rainer, “Fatigue investigation of higher strength structural steels in
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[11] E. Subramanian, Estimation of fatigue life of welded joint using vibration-fatigue
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[12] I. Poutiainen, P. Tanskanen and G. Marquis, “"Finite element methods for structural hot
spot stress determination - A comparison of procedures",” International Journal of Fatigue ,
vol. 26, no. 11, 2004.
[13] G. Li and Y. Wu, “A study of the thickness effect in fatigue design using the hot spot stress
method,” 2010.
[14] M. Heshmati, M. Al-Emrani and B. Edlund, “Fatigue Assessment of Weld Terminations in
Welded Cover-Plate Details,” Oslo, Norway, 2012.
[15] H. Remes and W. Fricke, “Influencing factors on fatigue strength of welded thin plates
based on structural stress assessment,” Weld World 58, p. 915–923, 2014.
59
[16] I. Poutiainen, “A modified structural stress method for fatigue assessment of welded
structures,” 2006.
[17] W. Fricke and O. Feltz, “"Fatigue Tests and Numerical Analyses of Partial-Load and Full-
Load Carrying Fillet Welds at Cover Plates and Lap Joints",” Weld World 54, p. R225–R233,
2010.
[18] Y. Kim, J.-S. Oh and S.-H. Jeon, “Novel hot spot stress calculations for welded joints using
3D solid finite elements,” Marine Structures, vol. 44, pp. 1-18, 2015.
[19] D. E. Djavit and S. Erik, Fatigue failure analysis of fillet welded joints used in offshore
structures, Chalmers University of Technology Department of Shipping and Marine
Technology, 2013.
[20] M. R. Pradana, X. Qian and S. Swaddiwudhipong, “A Revisit to the Effective Notch Stress
S-N Curve for Welded Circular Hollow Section Joints,” 2016.
[21] A. Göransson, Fatigue life analysis of weld ends, Linköping University, Department of
Management and Engineering, Division of Solid Mechanics, 2012.
[22] J.-M. Lee, J.-K. Seo, M.-H. Kim, S.-B. Shin, M.-S. Han, J.-S. Park and M. Mahendran,
“Comparison of hot spot stress evaluation methods for welded structures,” International
Journal of Naval Architecture and Ocean Engineering, vol. 2, no. 4, pp. 200-210, 2010.
[23] H. Kyuba and P. Dong, “Equilibrium-equivalent structural stress approach to fatigue
analysis of a rectangular hollow section joint,” International Journal of Fatigue, vol. 27, no. 1,
pp. 85-94, 2005.
[24] W. Fricke, “Round-Robin Study on Stress Analysis for the Effective Notch Stress
Approach,” Weld World 51, p. 68–79, 2007.
[25] W. Fricke, A. Kahl and R. H. Paetzold, “Fatigue Assessment of Root Cracking of Fillet
Welds Subject to Throat Bending using the Structural Stress Approach,” Weld World 50, p.
64–74, 2006.
60
Accuracy
Computational time
Multiple welds and
long welds
Flexibility/Robustness
Ease of
implementation
Meshing, preprocessing
Post-processing
Criteria
61
4
4
4
3
15
5
7.5
7.5
Total
score
Rank
1
0.225
3.925
0.3
0.6
0.2
Weight Hot spot
function Rating Weighted
‘w’
‘r’
score
(1-5)
‘w*r’
25
3
0.75
25
5
1.25
15
4
0.6
3
3
2
2
TTWT
Rating
‘r’
(1-5)
3
3
3
5
0.225
2.8
0.225
0.3
0.1
Weighted
score
‘w*r’
0.75
0.75
0.45
3
4
3
3
0.3
0.45
0.15
Weighted
score
‘w*r’
1.00
0.75
0.45
2
0.225
3.375
Dongs
Rating
‘r’
(1-5)
4
3
3
4
2
2
2
3
0.3
3.3
0.15
0.3
0.1
Xiao Yamada
Rating Weighted
‘r’
score
(1-5)
‘w*r’
4
1.00
4
1.00
3
0.45
4
2
1
2
4
0.3
2.9
0.15
0.15
0.1
Effective notch
Rating Weighted
‘r’
score
(1-5)
‘w*r’
5
1.25
2
0.5
3
0.45
Appendix A – Method scoring matrix
Appendix B – Workflow summary
62
Appendix C – Weld fatigue assessment tool interface
63
Appendix D – Structural stress approaches for further scope
Here are some structural stress methods with a brief introduction that can be considered for future
implementation as a plug-in tool.
Equilibrium-equivalent Structural stress (𝑬𝟐 𝑺𝟐 ) method
This method is like the through thickness linearization, but the structural stresses are calculated
along the weld line. The direction at which stress is calculated is perpendicular to the theoretical
plane of crack propagation along a weld line. The stress distribution over a plate thickness is nonlinear near the notch tip or weld toe due to presence of non-linear peak stress. But upon integration
through the thickness by considering self-equilibrium condition, the non-linear peak stress is
cancelled out thus the remaining bending stress, 𝜎𝑚 and membrane stress, 𝜎𝑏 contribute to the
structural stress of the weld [23].
The equilibrium condition excluding the non-linear stress peak is given by the equations below
where 𝜎𝑥 (𝑦) is the stress distribution and 𝑦 corresponds to a point in thickness axis direction:
𝜎𝑚 =
1 𝑡
∫ 𝜎 (𝑦)𝑑𝑦
𝑡 0 𝑥
6 𝑡
𝑡
𝜎𝑏 = 2 ∫ 𝜎𝑥 (𝑦) ∙ ( − 𝑦) 𝑑𝑦
𝑡 0
2
𝜎𝑆 = 𝜎𝑚 + 𝜎𝑏
The 𝐸 2 𝑆 2 is a stress index that is obtained after calculations of the results from an FEA by
considering equilibrium conditions at the weld toe. The calculated 𝐸 2 𝑆 2 is then plugged into a
master S-N curve to find the fatigue life of the model. This method yields the best results for shell
or plate element models and only requires the nodal forces due to elements obtained from the
command NFORC in ABAQUS.
Firstly, the nodal forces obtained with respect to global coordinate system is converted to local
coordinate system [23]. This nodal force, 𝐹𝑥 is further used to calculate the line force, 𝑓𝑥 and line
moment, 𝑚𝑦 using the shape function matrix where the variables 𝑙1,𝑙2 …𝑙𝑛−1 are the length of the
corresponding ith (i = 1 to n-1) element along the weld line. The inverse of the shape matrix is
found and multiplied to the nodal force matrix to find the line force. The shape matrix and the
procedures followed are same for finding the line moment as well.
𝑙1
3
𝑙1
6
𝐹1
𝐹2
𝐹3
= 0
⋮
0
⋮
{𝐹𝑛 }
⋮
[0
𝑙1
6
𝑙1 + 𝑙2
3
𝑙2
6
0
𝑙2
6
𝑙2 + 𝑙3
3
⋱
⋱
⋱
⋱
⋯
⋯
0
0
64
0
⋯
0
0
⋯
0
𝑙3
6
⋱
0
0
⋱
𝑙𝑛−2 + 𝑙𝑛−1
3
𝑙𝑛−1
6
0
𝑙𝑛−1
6
𝑙𝑛−1
3 ]
𝑓1
𝑓2
𝑓3
⋮
⋮
{𝑓𝑛 }
The line force and line moments are further divided by the thickness and section modulus to
obtain the bending stress and membrane stress which gives the structural stress when combined:
𝜎𝑠 = 𝜎𝑚 + 𝜎𝑏 =
𝑓𝑥 ′ 6𝑚𝑦 ′
+ 2
𝑡
𝑡
The equivalent 𝐸 2 𝑆 2 parameter, 𝑆𝑠 can be calculated by substituting the structural stress into:
𝑆𝑠 =
𝜎𝑠
2−𝑚′
𝑡 2𝑚′
1
∙ 𝐼(𝑟)𝑚′
where 𝑡 is plate thickness, 𝑚′ is the slope and 𝐼(𝑟) is a dimensionless function of bending ratio, 𝑟
that varies with the type of element and loading mode used in the analysis, and is generally given
by:
𝐼(𝑟) = 0.294𝑟 2 + 0.846𝑟 + 24.815
𝑟=
𝜎𝑏
𝜎𝑏 + 𝜎𝑚
The fatigue life 𝑁 can now be found by using the equation
𝑙𝑜𝑔𝑁 = 𝐵. 𝑙𝑜𝑔∆𝑆𝑆 + 𝐴,
where A and B are constants given in the table below.
Statistical basis
Mean curve
Upper 95% prediction
Lower 95% Prediction
Upper 99% prediction
Lower 99% prediction
A
12.185448
12.9285869
11.4423091
13.166404
11.24044912
B
-3.055853
Structural stress at the weld throat for root failure
Wolfgang Fricke (2006) [25] proposed methods based on linearization of stress through thickness
for fillet welds subjected to throat bending where the structural stress acting along a weld leg must
be determined. The linearized structural stress across the weld leg can be obtained through several
ways based on the type of model being used:
•
•
•
Linearization of stresses or forces directly in the leg section
Linearization of stresses or forces in the throat section to the leg section
Linearization of stresses or forces in the attached plate to the leg section
Linearization of stresses or forces in the weld leg section utilizes from the weld leg of the base plate
which is welded to the attached plate. The stress distribution or nodal forces from the weld leg
section is applied to the formula given below to find the structural stress.
𝜆
1 𝜆
6
𝜆
𝜎𝑚,𝑤 = ( ) ∫ 𝜎(𝑧)𝑑𝑧; 𝜎𝑏,𝑤 = ( 2 ) ∫ 𝜎(𝑧) (( ) − 𝑧) 𝑑𝑧
𝜆 0
𝜆 0
2
65
𝜎𝑠,𝑤 = 𝜎𝑏,𝑤 + 𝜎𝑚,𝑤
where 𝜎(𝑧) is the stress normal to leg section, 𝑧 is the coordinate along the weld leg line, 𝜆 is the
leg length, 𝜎𝑚,𝑤 is the membrane portion of structural stress in weld leg section and, 𝜎𝑏,𝑤 is the
bending portion of structural stress in weld leg section
When nodal forces are used, the formula becomes
𝜎𝑚,𝑤 = (
1
6
𝜆
) ∑ 𝑃𝑥,𝑖 ; 𝜎𝑏,𝑤 = (
) ∑ [𝑃𝑥,𝑖 (( ) − 𝑍𝑖 )]
2
𝑏∙𝜆
𝑏∙𝜆
2
where 𝑃𝑥,𝑖 is the nodal force perpendicular to the weld leg section, 𝑍𝑖 is the nodal point
coordinate and, 𝑏 is the distance of the nodal position in weld direction
Linearization of stress at weld throat to weld leg section takes place in the mid-plane between two
weld leg or otherwise known as weld throat. Weld throat is defined by the smallest distance between
the weld root and the surface of the weld. The corresponding perpendicular to the mentioned
section will be used in the formula to find the structural stress at the throat to weld leg section:
𝑎
1 𝑎
6
𝜆
𝜆
𝜎𝑚,𝑤 = ( ) ∫ 𝜎⊥ ∙ 𝑐𝑜𝑠𝜃 + 𝜏⊥ 𝑠𝑖𝑛𝜃 𝑑𝑠 ; 𝜎𝑏,𝑤 = ( 2 ) ∫ [𝜎⊥ (( 𝑐𝑜𝑠𝜃) − 𝑠) + 𝜏⊥ 𝑠𝑖𝑛𝜃] 𝑑𝑠
𝜆 0
𝜆 0
2
2
𝑎
1
𝜏𝑤 = ( ) ∫ 𝜎⊥ ∙ 𝑠𝑖𝑛𝜃 + 𝜏⊥ 𝑐𝑜𝑠𝜃 𝑑𝑠
𝜆 0
where, 𝑎 is the throat thickness, 𝑠 is the coordinate along the throat section and 𝜃 is the weld
flank angle. When using nodal force for finding stress the formula is:
𝜎𝑚,𝑤 = (
1
6
𝜆
) ∑ 𝑃𝑥,𝑖 ; 𝜎𝑏,𝑤 = (
) ∑ [𝑃𝑥,𝑖 (( ) − 𝑍𝑖 ) + 𝑃𝑧,𝑖 ∙ 𝑥𝑖 ]
2
𝑏∙𝜆
𝑏∙𝜆
2
𝜏𝑤 = (
1
) ∑ 𝑃𝑧,𝑖
𝑏∙𝜆
where 𝑃𝑥,𝑖 , 𝑃𝑧,𝑖 , 𝑥 and 𝑧 are nodal x-force and z-force at (𝑥𝑖 , 𝑧𝑖 ) where 𝑥 and 𝑧 are coordinates.
Linearization of stress using stress or force in the attached plate are categorized into two based
on whether the attached plate is perpendicular or parallel to the main plate.
The formulas for the two types:
a) Attached plate perpendicular to main plate
𝑡
𝜎𝑚,𝑤 = 𝜎𝑚 ( )
𝜆
𝑡
𝑡
𝑡
𝑡2
𝑡∙𝛿
𝜎𝑏,𝑤 = 𝜎𝑚 [3 ( ) + 6 ( 2 ) (𝑔 − ( ))] − 𝜎𝑏 [( 2 ) − 6𝜏 ( 2 )]
𝜆
𝜆
2
𝜆
𝜆
𝜏𝑤 = 𝜏
b) Attached plate parallel to main plate
66
𝑡
𝜆
𝜎𝑚,𝑤 = 𝜏
𝜎𝑏,𝑤
𝑡
𝜆
𝑡2
𝑡2
𝑡 𝛿
1
= −3𝜎𝑚 2 + 𝜎𝑏 2 + 6𝜏 (( ) + ( ))
𝜆
𝜆
𝜆 𝜆
2
𝑡
𝜏𝑤 = 𝜎𝑚 ( )
𝜆
67